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Name:______________________ Date:_________ Regents Physics Mr. Morgante

UNIT 5 Waves & Light

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WAVES AND LIGHT

Wave Properties Pulse- Single vibratory disturbance which moves from point to point through a medium. Wave- Several pulses generated at regular time intervals. Waves transfer energy without transferring mass.

Ex. - A slinky that someone shakes or wave in a rope, water waves and sound waves

Light, radio and other electromagnetic waves are periodic disturbances in an electromagnetic field. They need no material medium and can travel through a vacuum. The 2 most common types of waves are longitudinal and transverse waves. Longitudinal Waves- particles vibrate parallel to the direction of the wave motion. Sound is an example of this. Seismic Waves (P-waves) are longitudinal waves. They are made up of compressions (where particles are close together) and rarefactions (where particles spread out).

• Most people don’t usually picture this kind of wave when they think of a wave. • Imagine securing one end of a Slinky to a wall.

o Now stretch out the Slinky by holding onto one end and walking backwards.

o Stop walking. While holding onto the end still, bunch up some of the coils in your hand. Let go.

o The Slinky will “spring” back and forth away and towards you. There are areas where the Slinky is scrunched, and parts where it is stretched out. The “spring” or wave is moving parallel to the direction the particles are moving.

• In this wave, the particles are moving left and right parallel to the motion of the wave.

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• The best example of this kind of wave is sound. o Think about it… when you talk you are pushing, and sometimes not

pushing, air out of your lungs past your vocal cords. There will be parts where the air particles are squished together, and others where they are not pressed together that close.

Transverse Waves- Particles vibrate perpendicular to the direction of the waves. Electromagnetic waves such as light and radio are examples of transverse waves. Seismic waves (S-waves) are transverse waves. Transverse waves can travel in the same direction but in different planes.

• These are the waves that have the classical wave shape.

Wave Characteristics

Frequency When we first started looking at SHM we defined period as the amount of time it takes for one cycle to complete... e.g. seconds/cycle

• Frequency is the same sort of idea, we’re just going to flip things around. • Frequency is a measurement of how many cycles can happen in a certain amount of

time… e.g. cycles/second. • If a motor is running so that it completes 50 revolutions in one second, I would

say that it has a frequency of 50 Hertz. • Hertz is the unit of frequency, and just means how many cycles per second. It is

abbreviated as Hz. • In formulas frequency appears as an f.

Since frequency and period are exact inverses of each other, there is a very basic formula you can use to calculate one from the other…

f = 1 / T or T = 1 / f

Example: The period of a pendulum is 4.5s. What is the frequency of this pendulum? The period means that it will take 4.5 seconds for the pendulum to swing back and forth once. So, I expect that my frequency will be a decimal, since it will complete a fraction of a swing per second.

f = 1 / T = 1 / 4.5s = 0.22 Hz

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Wavelength Wavelength is a property of a wave that most people (once they know what to look for) can spot quickly and easily, and use it as a way of telling waves apart. Look at the following diagram:

Any of the parts of the wave that are pointing up like mountains are called crests. Any part that is sloping down like a valley is a trough.

• Wavelength is defined as the distance from a particular height on the wave to the next spot on the wave where it is at the same height and going in the same direction. Usually it is measured in metres, just like any length.

• There isn’t a special spot you have to start on a wave to measure wavelength, just

make sure you are back to the same height going in the same direction. Most people do like to measure from one crest to the next crest, just because they are easy to spot.

• On a longitudinal wave, the wavelength is measured as the distance between the middle of compressions, or the middle of expansions.

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This leads us to one of the most important formulas you will use when studying waves.

• Frequency tells us how many waves are passing a point per second. • Wavelength tells us the length of those waves in metres. • If we multiply these two together, we are really multiplying 1/s and m… which gives

us m/s, the velocity of the wave! Velocity of a Wave

v = f λ v = velocity of the wave (m/s) f = frequency (Hz) λ = wavelength (m)

Velocity is the speed of the wave. The medium that the wave travels through determines its velocity (i.e. air vs. water). Units are (m/s). Velocity = frequency * wavelength V = f λ Speed The speed of a wave is the distance traveled per unit time by any part of the wave. Speed is generally expressed in meters per second and is symbolized by v. The speed of a wave depends on the nature of the medium through which it travels. Sound waves, for example, travel faster in warm air than in cold air. The relationship between the speed of sound and the temperature of the air is provided by the formula v = 331 + 0.6T, where v is the speed of sound in meters/second and T is the temperature in ΕC. Some materials allow waves of different frequencies to travel through them at different speeds. Such media are called dispersive. Glass is a dispersive medium for light waves. The speed of a light wave is also equal to the product of its frequency and wavelength. Example: If 5 cycles pass a given point in one second and each cycle is 2 meters long, then 10 meters of “wave” pass the point per second. The frequency (f) is 5 Hz, the

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wavelength (8) is 2 meters, and the speed is 10 meters per second. Example: A wave is measured to have a frequency of 60Hz. If its wavelength is 24cm, how fast is it moving?

v = f λ = (60Hz) (0.24m) v = 14 m/s

Example: The speed of light is always 3.0 x 108 m/s. What is the frequency of red light, which has a wavelength of 700nm?

Be careful when changing the 700nm into metres. Some people get really caught up with changing it into regular scientific notation with only one digit before the decimal. Why bother? You’ll probably just make a mistake changing the power of 10, so just substitute in the power for the prefix and leave everything else alone…700 nm = 700 x 10-9 m since “nano” is 10-9. v = f λ f = v / λ = (3.0 x 108m/s) / (700 x 10-9m) f = 4.3 x 1014 Hz

Amplitude Amplitude is a measure of how big the wave is.

• Imagine a wave in the ocean. It could be a little ripple or a giant tsunami. • What you are actually seeing are waves with different amplitudes. • They might have the exact same frequency and wavelength, but the amplitudes of the

waves can be very different. The amplitude of a wave is measured as:

1. the height from the equilibrium point to the highest point of a crest or 2. the depth from the equilibrium point to the lowest point of a trough

When you measure the amplitude of a wave, you are really looking at the energy of the wave. It takes more energy to make a bigger amplitude wave. Amplitude of a wave is related to energy of a wave.

• Anytime you need to remember this, just think of a home stereo’s amplifier… it makes the amplitude of the waves bigger by using more electrical energy.

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As amplitude of light wave increases so does its brightness. As amplitude of a sound wave increases, so does the loudness. Period- Time for one complete cycle to pass a point. Period is the reciprocal of frequency and is calculated from the formula T-1/f, where (T) is period and (f) is frequency. Phase Points on a periodic wave that are identically displaced from the equilibrium position and are moving in the same direction away from the equilibrium position are said to be in phase. In other words, the phase difference between them is 00. Points that are in phase are always a whole number of wavelengths apart. Points on a periodic wave that are equally displaced from the equilibrium position but are moving in opposite directions are said to be 1800 out of phase. Points that are 1800 out of phase are always an odd number of half wavelengths apart. See next page. Pt. A Pt. B

Pt. D Pt. E Note: Pts. A&B, C&D, and D&E are all in phase. A&C, A&D, etc, are out of phase. Boundary Barrier When a wave encounters a boundary between two different media, part of the wave is reflected back into the first medium. The fraction of the wave’s energy that is reflected and the fraction transmitted depend on the type of wave and on the nature of the two media. For example, when a light wave traveling through the air hits glass, most of the wave’s energy is transmitted through the glass and only a small fraction is reflected. On the other hand, when a water wave reaches the end of a pool or lake, or when a sound wave encounters a smooth rigid wall, most of

Pt. C Pt. D

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the wave’s energy is reflected back into the first (or original) medium. The part of the wave that is reflected at the boundary between two media retains the same speed, frequency, and wavelength as the original wave. The part of the wave that is transmitted into the second medium, however, experiences a change in speed, since the speed of a wave is determined by the medium. The transmitted wave’s frequency, on the other hand, is determined by its source and does not change. Since wavelength, frequency, and speed are interrelated (v = f λ), a change in speed must result in a change in at least one of the other two factors. If the frequency remains constant there must be a change in wavelength when the wave enters the second medium. For example, the speed of light in glass is less than it is in air; this means that the wavelength of light becomes shorter as it passes from air to glass. The speed of a wave does not depend on the amplitude or frequency of a wave.

• Instead, the speed of the wave is determined by the properties of the medium it is traveling in. o “Medium” is the substance the wave is traveling through (plural = media). For

example, the normal medium for sound is the air. o Examples of the properties of media effect on speed:

Speed of water waves depend on the depth of the water. Speed of waves in a rope depend on the force exerted on the rope and the

weight of rope used. Speed of sound in air depends on the temperature of the air.

• A wave with a bigger amplitude does transfer more energy, but it will still travel at the same speed as a smaller amplitude wave in that same medium.

Quite often a wave will move from one medium to another, like sound traveling through the air and then into water.

• This will definitely change the speed of the wave, and may also cause it to be somewhat distorted (changed randomly). We will assume no distortion happens in our examples. o The original wave that came moving in through the first medium incident

wave o The wave that continues into the new medium transmitted wave o Any wave that bounces back reflected wave

• Different things will happen when the incident wave hits the boundary between the two media, depending on the densities of the media compared to each other…

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Change in Density BIG If there is a big difference between the densities of the media, the following will happen:

1. The incident wave will come moving in towards the boundary.

2. When it hits the boundary, almost all of the wave will be reflected back the way it came! Almost none of the wave will be transmitted.

Notice that the reflected wave is still right side up (we call this “erect”)… why?

This is a question of what happens when the wave is going from more to less dense media, compared to less to more dense media.

• If the wave is going from a more to less dense media then the reflected wave is erect (same side up). o Any part of the wave transmitted will still be erect and speeds up.

• If the wave is going from a less to more dense media then the reflected wave is inverted (upside down). o Any part of the wave transmitted will still be erect and slows down.

Example: I hang a giant slinky spring from the ceiling (using very light string). I then make a wave travel through the slinky towards the other end, which is just dangling there. Describe the waves at the boundary.

• The change from the original media (the spring) to the second media (the air) is definitely a BIG change in density, so most of the wave will be reflected back through the slinky.

• Since it is going from more to less dense, the reflected wave will be erect. • The little bit of the wave that is transmitted into the air will be erect and speed up.

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Change in Density SMALL If the change in density is small, things are a lot easier to remember.

• Quite simply, almost all of the incident wave will be transmitted and stay erect.

• It’s hard to see the boundary between the two media in the middle, but they are

slightly different densities (thickness of line).

• That’s it! The transmitted wave is (almost) the same as the original incident wave.

o Only a very little bit of the wave will be reflected (I didn’t even bother drawing it in).

The Doppler Effect Although it is generally true that the number of cycles passing by a given point per second (the observed frequency of a wave) is equal to the number of cycles produced by the source per second (the transmitted frequency), this is not the case if the source and the observer are moving relative to each other. When the source and the observer approach each other, the number of cycles observed passing by per second is greater than would have been the case had the source been at rest. In this case, the observed frequency is greater than the transmitted frequency. When the source and observer move away from each other, the number of cycles observed passing by per second is less than would have been the case had the source and observer been at rest. In this case, the observed frequency is less than the transmitted frequency. These phenomena are known as the Doppler effect, and important consequences result from them. The pitch of a sound wave, a quality that is related to frequency, changes noticeably as the source of a sound, such as a siren or radio, first approaches the observer, passes by, then recedes. In the case of light waves, the Doppler effect leads to changes in color. White light from an approaching source, for example, takes on a bluish appearance. From a receding source, the light shifts toward the red. The amount of increase or decrease in frequency that results from relative

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motion between a source and an observer is dependant upon the speed of the source or the observer or both. Indeed, it is possible to determine the unknown speed of a source of sound or light, toward or away from the observer, from the change in pitch of the sound or change in color of the light. Doppler Effect (in other words)- This effect is observed when the source or the

observer is moving. There is an increase in the observed frequency when the vibrating source approaches the observer. There is a decrease in observed frequency as the source moves away from the observer.

-If a source is moving at a constant velocity, the frequency heard as it comes towards you will be a constant higher frequency than produced by the source. If the source is moving away , the frequency heard is constant but lower than the produced source. -If the source is accelerating towards you, the frequency will be higher and will be lower and continue to get lower.

• Here the insect is “cathing up” to the sound waves it emits so the pitch will increase if you are standing in front and the insect is moving toward you. The pitch will decrease once the insect passes you and continues to move away.

Interference - The effect produced by two or more waves which are passing simultaneously through a region.

o Superimposed just means to put something on top of something else, or blend two things together.

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o When we are talking about waves, we mean that two or more waves are passing through the same area and have a temporary effect on each other.

o Their amplitude will change for that brief moment, but as soon as they pass, they go back to their original sizes.

We will follow a very simple rule (even if it sounds confusing), called the “Principle of Superposition.”

“The displacement of a medium caused by two or more waves

is the algebraic sum of the displacement of the waves” How do we break down what this means?

• “Displacement of the medium” just means how big the amplitude of the waves will be.

• “Algebraic sum” is just the simple addition of numbers… 2 + 3 = 5 or maybe 4 + -3 = 1. This is just how we will add the amplitudes.

• Some examples would probably make more sense. Example: These two wave pulses are moving towards each other. What will happen when they are on top of each other?

• Notice that wave A has an amplitude of 2, while wave B has an amplitude of 1. • Both of the wave pulses are erect, so we say that they have positive values for

amplitudes. • As they come together in the middle, both of them are pulling particles of the medium

upwards…

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• When they are directly over each other, they are both shoving particles up together, so

the two waves become one big wave with an amplitude of 3 for an instant.

• They are still two separate waves, they just happen to be in the same spot at the same

time. • They will continue moving on and look exactly the way they looked before they hit

each other.

• This is an example of Constructive Interference. o The two waves interfered with each other, but did it in such a way that they

constructed something bigger than either of them alone. We usually think of things hitting as destroying each other permanently.

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• This is not the case for waves, since the waves themselves are not made of matter, they only travel through matter.

• Waves might temporarily “destroy” each other, but as soon as they pass each other they will go back to their original appearance.

Example: These two wave pulses are going to collide. What will happen?

• Notice that A and B are still the same amplitude, but now B is inverted. • Can you understand why when these two wave pulses are on top of each other that

they would look like this…

• For a moment the two wave pulses become one smaller wave pulse with an amplitude

of (+2 + -1 = +1) positive one. • As soon as they have passed each other…

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• Since the two waves together are smaller than they would be on there own, we call this

Destructive Interference. There are also other situations where you can observe constructive and destructive interference as shown below. Acoustical engineers need to consider this situation during concerts because where a crest and a trough intersect, the people in the audience will not hear anything!!! They want to achieve maximum constructive interference everywhere!!!

You now see how waves can build each other up, or rip each other down, at least momentarily. So what’s the big deal?

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• There was actually a very real concern if you were in the Roman army a couple thousand years ago…

According to legend, a large number of Roman legionnaires were moving from one location to another by foot (sorry, no buses back then!). They had to cross a rather large bridge to get across a large river. As they crossed the bridge, they continued to walk as every good legionnaire is trained to… in sync. Left, right, left, right, etc. You can imagine that this started some waves shaking through the bridge. Unfortunately for the legionnaires they were walking in just the right (or I guess from their view, wrong) way that the waves they were creating with their marching were adding onto each other constructively. The amplitude of the waves increased rapidly until the bridge finally collapsed under their feet! Most of them died from the fall or drowned in the water.

Resonance To understand the special type of constructive interference that was happening, think of the following situation.

• You tie off a piece of rope to the wall, and then stretch it out. • Standing at the far end you flick your wrist to send a wave pulse to the other end. • When the pulse hits the wall most of it will be reflected back towards you as an

inverted wave. • If you just held tightly with your hand, the wave would hit your hand and most would

be reflected away from you as an erect pulse… instead, you flick your wrist again at exactly the instant that the first wave hits. o The two waves are now both traveling away from you, both erect, and both on top

of each other. Their amplitudes will add together to make a bigger wave! • Keep doing this over and over again and the wave keeps getting bigger.

In the above example you are making sure that the frequency of your wrist flicks matches the frequency of the wave itself.

• We give this special kind of constructive interference a name: Resonance • In any of these examples (the soldiers, the rope, etc.), the frequency of the wave it self

is equal to the frequency of new waves being created. We would say that the new waves are being created at the “resonant frequency”.

• Another example of resonance would be swinging someone on a swing. o You make sure to push them only as they are swinging away from you. That way

they go higher and higher. o If you just randomly pushed at them, you wouldn’t help them go any higher.

• You might even have heard of someone singing to break a wine glass… it is recorded as having been done once, and they didn’t have to sing loud, just at the resonant frequency of the glass.

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Standing Waves Standing waves are just an extension of the concept of resonance.

• Suppose you now made sure the wavelength of the wave you made in the rope example above was exactly double the length of rope. o You would get something that would look like the bottom part of the picture in

Figure 14-16 (p.298) in the text. • Now double the frequency, and you get something like the middle image of figure 14-

16, and so on. • In each of these examples you are creating a wave that just seems to be sitting there

bouncing up and down. • We call these standing waves.

o Any part of the wave that never moves is called a node. o Any part that has maximum amplitude is called an antinode.

Wave Nature of Light Behavior of light can be interpreted in terms of wave phenomena. Interference phenomena, as previously discussed, can be produced by light. (Coherent source - light from one source) w/same phase relationship Diffraction- Spreading of a wave into a region behind an obstacle.

Node

Antinode

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Speed of Light C=f λ ; similar to V=f λ except now C=Speed of Light C in Ref. Table front sheet = 3.08 * 108 m/s Or 3 * 108 m/s = 186,000 mi/sec This holds true in a vacuum or outer space medium (air) Diffractive mediums (or other mediums) have the capability to slow down the speed of light.

Reflection There is nothing really mysterious about reflection, but some people try to make it more difficult than it really is. To be able to show you a drawing to learn the main principles of reflection we first need to define a word: normal.

• You might remember this word from when we studied forces. We say that a line drawn at 90° to the surface is a normal line.

• When you want to figure out how something will reflect from a surface, draw a normal line to that surface at that point.

After you’ve done that there is only one rule to remember…

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The angle of incidence equals the angle of reflection.

• The angle that we are referring to is the angle between the normal line and the wave coming in. An example will probably make this simple for you to understand.

• Notice how the incident wave coming in is at an angle of 42° from the normal. When it

reflects off the surface it bounces off at an angle of 42°. The two angles are equal! The only time you need to be really careful with the law of reflection is when the surface is somehow irregular.

• You still draw normal lines, you just have to be very careful that it is at 90° to the surface at that point.

• If the surface is curved (which we will examine later), you will draw a whole bunch of normal lines for many points on the surface.

• You still draw the incident and reflected waves the same way relative to the normal lines,

you just have to be careful about how you draw those normal lines. • Sometimes you might have a surface that is really irregular… a whole bunch of random

bumps. You still draw normal lines, but they’ll be pointing in all sorts of weird directions.

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Θi

Refraction Definition: Refraction is the change in direction of a wave that occurs when

the wave passes obliquely through a boundary (aka interface) and across which there is a change in speed.

Normal

Incident Ray Speed here = C

Medium 1 (Air) Boundary Interface

Medium 2 (Glass) Refracted Ray Θr Speed here < C Figures 1 & 2 Above – Light Wave going from a less dense to a denser medium. Note the light ray refracts towards the normal since it is being slowed down. If the light ray were going from glass to air, the diagram above would look similar except that the light ray would increase its speed as it comes out into the air medium and would therefore speed up and away from the Normal. The Normal is just a perpendicular line between the two mediums where the incident and refracted light rays are located.

• Have you ever looked at something like a pencil or pen sitting in a cup of water? It probably looked something like this on the next page…

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• Notice how the pen looks like it is bent and bigger in the water… something must be happening to the light waves as they travel through two different substances… water and air.

Again……… Effect of the medium: The speed of light waves depends on the properties of the medium. Speed and Refraction 1. When a wave enters a new medium obliquely, and there is a decrease in

speed, the wave bends towards the normal (Forms a smaller angle) 2. When a wave enters a new medium obliquely, and there is an increase in

speed, the wave bends away from the normal (Forms a larger angle) Definitions: Polychromatic light contains waves of different frequencies. Polychromatic light may be dispersed because each frequency of light has a different absolute index of refraction. Monochromatic Light contains light of just one frequency.

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Absolute Index of Refraction Snell’s Law Have you ever looked at someone standing in the shallow end of a swimming pool and thought that they looked really short? As soon as they stepped out they looked taller.

• Something must be happening to the way that light is traveling to your eyes. • Your brain and eyes always assume that the light is traveling to your eyes in a straight

line… which is not always the case! • This does not mean that light travels in curved lines, but the direction that a beam of

light is traveling can be changed. What is really happening is refraction, the bending of waves as they pass from one medium to another.

• In the swimming pool example, the light traveling through the water from the person’s feet must be bending and moving in another direction when it enters the air… this makes their feet appear to be in a different spot making the person look shorter.

• Since Ptolemy’s time (about 100AD) people knew about refraction, but they didn’t know why it happened, or how to predict and calculate it.

In the year 1600 a Dutch mathematician named Willebrord Snell was playing around with numbers and figured out a formula that fit what everyone was measuring.

• The Law of Refraction (AKA “Snell’s Law) in its basic form allows us to do calculations of how a beam will bend when it moves from one medium to another.

• We will refer to the first medium as a subscript “one” on the formula, the second medium as a subscript “two”

n1 sinθ1 = n2 sinθ2 θ = angle from normal

n = index of refraction for medium

• We will usually be describing refraction in terms of whether the beam of light bends away from or closer to the normal. • Going from more dense to less dense bend away • Going from less dense to more dense bend towards

The index of refraction (n) is a way of comparing the “optical density” of different materials.

• Think of optical density as how easily light can travel through the material.

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• A low index of refraction (like water nw =1.33) is pretty easy to travel through. • A high index (like diamond nd = 2.42) is difficult for light to travel through.

• The index of a material is usually measured in an actual experiment… there’s no reliable way to just predict what they will be.

• Index of refraction has no units and is based on how light travels in a vacuum.

Medium Index of Refraction Vacuum 1.00 Air 1.0003* Water 1.33 Ethanol 1.36 Glycerin 1.47 Crown Glass (varies slightly) 1.50 – 1.62 Quartz 1.54 Flint Glass (varies slightly) 1.57 – 1.75 Diamond 2.42

*but go ahead and just use 1.00 Example: A beam of light traveling in glycerin hits the boundary between itself and water at an angle of 43° from the normal. What angle will it travel through the water?

• Just like in the examples we did earlier in the waves section, we can call the original beam traveling in the glycerin the incident ray, and the light traveling in the water the refracted ray.

• We can look up the indices for glycerin and water from the table above and figure out the angle… we can call either of them “one” and the other “two” as long as we stay consistent. I’m going to say glycerin is one and water is two.

n1 sinθ1 = n2 sinθ2 1.47 (sin43°) = 1.33 (sinθ2) θ2 = 49° make sure your calculator is in degree mode!

• The diagram would look something like this… The formula for Snell’s Law doesn’t look like this in your data sheet, since we’ve expanded it so you can do more things.

1

2

2

1

2

1

2

1

nn

vv

sinsin

=λλ

==θθ

The weird thing about this formula is that you don’t use it all at once in a question.

• You only ever use two terms in any one question. • We will usually give you three pieces of information and then you have to solve for

the fourth.

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Example: A beam of red light (λ = 700nm) is traveling through water (n = 1.33). If it leaves the water and travels into a piece of flint glass (n = 1.75), what color (approximately) will it be?

• You don’t see this color change for regular light, since regular white light has all of the colors of the rainbow and a shift in wavelength doesn’t change anything overall. Using a pure color (like from a laser) can result in a noticeable color shift.

• We will only use the part of the formula that has wavelengths and indices.

1

2

2

1

nn

=λλ

75.1)33.1)(m10x700(

nn 9

1

221

−

=λ

=λ

λ1 = 5.32 x 10-7 m

• A wavelength of 5.32 x 10-7m is the same as 532nm. This makes it a greenish color, maybe a little on the yellowish–green side.

Speed of light Notice in the formula that the velocity of light will change in different media.

• The speed of light is a constant in one particular medium. • Switch to a different medium and the speed of light will be a different constant in that

medium. • The speed that we use (3.00 x 108m/s) is the speed of light in a vacuum. • Scientists have successfully slowed light down to about 1 km/h! Although this is

tough to do, it is possible. • It is even possible for light to go faster if it is in a medium with an index of refraction

less than 1.0. • This does not break Einstein’s rules about the speed of light being the fastest

speed, since he said no thing (with mass) can go faster than 3.00 x 108m/s… light doesn’t have mass!

This is actually one of the best ways to measure the index of refraction for an unknown material.

• Have light traveling initially through a vacuum enter the substance and measure its speed. From that you can calculate the index of refraction.

Example: A student is doing a lab. They test a material that light travels at 2.21 x 108m/s through. What might the substance be?

1

2

2

1

nn

vv

=

25

s/m10x21.2)00.1)(s/m10x0.3(

vnvn 8

8

2

112 ==

n2 = 1.36

From the chart we have a substance with an index of refraction of 1.36 could be ethanol. There might be other substances with this same index, so we can’t be sure.

Total Internal Reflection The bending of light as it travels from one medium to another has an interesting effect on light leaving an optically dense medium into a less dense medium.

• Let’s look at what happens to the refracted angle as we increase the incident angle slowly for a ray leaving a more optically dense substance into a less optically dense…

Red Beam

Notice that the red beam does exactly what we would expect it to do. It leaves the water and bends away from the normal.

Blue Beam

We’ve increased the angle that the beam is traveling through the water. This means that the beam leaves the water and travels into the air at a bigger angle away from the normal. Notice that the beam traveling in the air is getting closer to the surface of the water.

Green Beam

This beam is traveling through the water at a pretty big angle from the normal. In fact, it is traveling at such a big angle from the normal that when the beam tries to leave into the air, it is refracted at 90°!!! This means that the beam never really leaves the water, but instead skims along the surface of the water. For this reason we call the angle that the beam is traveling in the water its critical angle with air. We can calculate this angle using the following method…

1

2

2

1

nn

sinsin

=θθ

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33.1)00.1)(90sin(

nnsinsin

1

221

°=

θ=θ

sinθ1 = 0.752 θ1 = 49°

This is the critical angle for water to air. Any other combination of media you would have to calculate a new critical angle for. Notice also from the formula that this can only happen if something is going from higher to lower density substances.

Purple Beam

For any angle bigger than the critical angle you just calculated, the beam can’t even leave the water. It will be refracted so much that it actually just starts to reflect. This is the total internal reflection that we were talking about in the title for this section. Just use the regular rule for reflection… whatever the incident angle is, the reflected angle will be the same.

This is actually the principle used in fiber optic cables.

• The fiber optic cable itself is made of a material like Plexiglas, part plastic and part glass. It is slightly flexible, although if you bend it too sharply it will snap.

• A light beam shinning in one end of the fiber will bounce off of the inside surface because of total internal reflection with very little loss.

• The beam coming out the other end is very strong, even if the cable is hundred of kilometres long.

Plane Mirrors “Plane” in this case refers to “flat”.

• If the mirrors were not flat we would have to use more complicated rules (more on those later in the course).

• Doing problems involving plane mirrors is actually pretty easy since we only have to remember a few things: 1. The law of reflection:

o Any light beam that hits the mirror will bounce off at exactly the same angle. o We assume the mirror is perfect in theses situations. o We will have to make sure that the light rays reflected off the mirror hit the

observers eye. 2. In a plane mirror the image will be the same size as the original object, and it will appear as far behind the mirror as the object is in front of the mirror.

The only challenge (and it’s not a very big one) is figuring out how your eye/brain interprets the information and where the reflected object appears to be.

• Let’s look at a simple example to illustrate how I would draw it on the next page…

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1. Measure how far the object is in front of the mirror. Draw a quick sketch of the image

behind the mirror at the same distance (just make sure it’s flipped around). 2. Draw a line from the observer’s eye to an important part of the image (like the top). The

line should be dashed when it is behind the mirror to show that the light ray isn’t really there.

3. At the point where that light ray hit the mirror, bounce it back at the same angle (law of reflection) so that it hits the same spot on the original object.

This gives you an idea of how the light rays are traveling from the object to you eye, and also why the image appears to be behind the mirror.

• Because the image of the object isn’t really behind the mirror (meaning that there are no true light rays that are back there), we refer to it as a “virtual image”. o You can always do a test in your head to determine if you are dealing with a virtual

image. Ask yourself “If I put a piece of paper where I think the image is (in the example above that would be behind the mirror), will I see the image on the paper like a film on a movie screen?” If the answer is “no”, you have a virtual image.

o Sometimes the answer can be “yes” when dealing with curved mirrors, a topic coming up soon. We’ll look at what happens in those situations then.

• When doing your sketches it is usually a good idea to do at least two points on the object to make sure that everything makes sense. In the example drawn above it would probably be best to draw some lines for the bottom of the moon shape. o Try sketching this one out on your own to see if you can remember the steps

correctly. Polarization Light is basically a bunch of transverse waves pointing in all sorts of directions all at once.

• Imagine a regular fence made out of boards that are vertical. I put a piece of rope through the space between two of the boards.

• Now stretch out the rope and get a friend to hold on to it on the other side. • You grab the other end and shake it up and down to make waves that move vertically.

o Will your friend on the other side see the waves coming towards him? Yup! Since the waves are vertical, they will pass through the vertical spaces in the boards.

• Now try shaking the rope side to side.

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o The waves will never reach your friend on the other side (even though he might see the rope shake a bit), since horizontal waves can’t travel through a vertical opening.

This is what polarization is all about. Waves of light are traveling up-down, side to side, diagonally back and forth, all at once.

• If you were to look at a beam of light coming straight at you and see its waves, you’d see something that looks like this…

• This is what the waves look like normally. We call it unpolarized light. • A piece of Iceland spar and tourmaline would remove most of the waves vibrating in

every direction, except one. • In a polaroid filter there are long molecules aligned parallel that act almost like the

fence boards in the example above. o When the light goes through the Polaroid filter only waves parallel to the

molecules in the polaroid filter will be able to pass through. o If the Polaroid filter is vertical, then the only waves to get through would be…

This is actually very useful for photographers to know about. • When light hits a shiny surface like water, it will reflect with its waves polarized

slightly. • This is because the waves that are vibrating in the direction that first hits the

surface get scrunched a bit.

• We see this scrunched polarized light as a glare from the surface.

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• To reduce the effect of the glare if I was taking a picture in these conditions, I would put a polaroid filter on the camera so that it is aligned vertically. o Although it won’t get rid of all the horizontal waves, it will get rid of enough so

that the waves are about equal. This will get rid of the glare.

Electromagnetic Spectrum Just like any wave, EM waves have particular wavelengths and frequencies. • Since the velocity of any EM wave is always 3.0 x 108 m/s (in vacuum), if you know one of the values, you can calculate the other using the formula v = fë. • Because the velocity of light is such an important constant, we use the symbol “c” to represent it. • You do NOT have to memorize this entire table of facts, figures, and numbers. • You do need to know the order of the different types of EM waves (radiation) and some basic facts about each.

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Low Frequency AC • Very weak, low frequency waves given off by any electrical appliance in your home. • You might have noticed warning labels on electronics about it interfering with radio signals.

o For you in your home, the biggest worry is that there will be static on your cordless phone when somebody turns on the vacuum cleaner.

o The government has regulations about how strong the interference of any one electronic device can be.

! Since we’re talking about strength of waves, we really are talking about the amplitude of the wave.

o Look at the beginning of the manual of something you own (like a CD player) for a “FCC Notice” that talks about interference.

Radio, Radar, TV Signals

• These are quite a jump up in frequency, but still only at most 1010Hz.

• These are the signals that are used by cell phones, cordless phones, radios (AM and FM), and TV signals that you get with an antenna.

• They are used because these (relatively) low frequencies are easy to generate.

Microwaves

• Yep, these are the ones you use to cook food.

• They’re called “microwaves” because as the frequency has been increasing the wavelength is going down.

o We’re actually going to deal with wavelengths much smaller than this as we continue, but this is the name given to these waves, so we use it. • Microwaves are also used to send radio and TV signals over long distances without losing quality. o This is possible because microwaves can be more carefully “aimed” at their destination.

Infrared Radiation

• If you feel heat from the sun or while under a heater in the LRT station, your feeling IR radiation.

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• IR actually causes electrons in the outer part of atoms to jiggle around a bit… sort of. • Besides using lamps to keep hamburgers at McDonalds warm, IR radiation is given off by any object in different amounts. o We can use devices like IR goggles to see an object in the dark.

VISIBLE LIGHT - Good old Red, Orange, Yellow, Green, Blue, Indigo, and Violet… ROY G BIV, the stuff we can see.

• Visible light happens when electrons make big jumps around inside the atom.

• Only covers a very small range of frequencies, from about 4 x 1014Hz to 8 x 1014Hz.

• You need to remember that red is the lower frequency (ë = 700nm), to green in the middle (ë = 500nm), to violet at high frequencies (ë = 350nm).

Ultraviolet Radiation

• Just past violet on the visible spectrum.

• No, this is not what you see with those “black lights” … you can’t see UV radiation!

o But those lights actually give off lots of UV… nasty!

• Causes tanning in human skin, but can also cause cancer.

o You actually need some UV radiation to allow your body to make vitamin D.

X-Rays

• Able to pass through less dense materials (like flesh), but can’t get through dense material (like bones and teeth).

• Safe in low doses, but prolonged exposure over a long time can damage cells.

o This is why a dentist steps out of the room when he takes an x-ray, otherwise he’d be exposed to x-rays hundreds of times a day for many years.

o It is also why airline pilots and flight attendants need to take a break from flying every so often.

• When you’re in a plane, with less atmosphere between you and space, you are exposed to more x-rays.

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Gamma Rays - Come from radioactive decay of atoms o This is the dangerous “radiation” you always hear about when talking about nuclear reactors and bombs. • Used as radiation therapy for some types of cancer. • Exposure to these high frequency, high energy EM waves is extremely dangerous.

Cosmic Rays

• These are the highest frequency, highest energy EM waves on the EM spectrum.

• They are created when super high energy particles hit Earth’s atmosphere.

• Very dangerous to living things.

Though electromagnetic waves exist in a vast range of wavelengths, our eyes are sensitive to only a very narrow band. Since this narrow band of wavelengths is the means by which humans see, we refer to it as the visible light spectrum. Normally when we use the term "light," we are referring to a type of electromagnetic wave which stimulates the retina of our eyes. In this sense, we are referring to visible light, a small spectrum of the range of frequencies of electromagnetic radiation. This visible light region consists of a spectrum of wavelengths, which range from approximately 700 nanometers (abbreviated nm) to approximately 400 nm; that would be 7 x 10-

7 m to 4 x 10-7 m. This narrow band of visible light is affectionately known as ROYGBIV. Maybe you remember this from chemistry.

Check out the following applet http://www.phy.ntnu.edu.tw/java/emWave/emWave.html For a demonstration of electromagnetic wave propagation.

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NAME________________________________ DATE________ Regents Physics Wave Notesheet Mr. Morgante Definitions: 1. Wave: 2. Medium: 3. “Every wave has, as its source… a. Methods of producing waves: Sound waves:_____________________________________________________ Radio wave: 4. “Waves transfer ______________ from one place to another by of a field.” 5. Mechanical wave propagation requires a .

a. Examples: 6. Electromagnetic waves:

(list at least 5 from the Electromagnetic Spectrum sect. RegRefTable) __________, __________, __________, __________, __________ can travel through a ____________, which is a region of empty space. Electromagnetic waves can also travel through:____________________________

7. Pulse:

a.Speed of pulse versus medium: Medium is a uniform material with the same property throughout, Pulse speed is:________________ b. Pulse reaches an interface or boundary of a new medium,

part of the pulse is____________________, part is ____________________, part is _____________

8. Reflection: 8a. Re-draw Figure 5-2 below and explain the reason for the inversion of the pulse:

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A Reason for inversion: B 9. Periodic wave: 10. Compare and contrast LONGITUDINAL & TRANSVERSE Longitudinal wave Transverse wave Definition: Examples: Labeled sketch: Summary: Waves transfer ____________ only. Sound waves cannot travel through a _____________.

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NAME________________________________ DATE________ Regents Physics Wave Notesheet , Part II Mr. Morgante Definitions: 1. Cycle: 2. Frequency:

a. “The frequency of a sound wave determines its______________, whereas

the frequency of a light wave determines its______________.” 3. Hertz (Hz):

a. Human sensory capabilities: “The human ear can detect frequencies in the range of _________________.” The human voice range_______________________. “…the human eye perceives frequencies of __________________________.”

4. Period: 5. Amplitude: a.Another term for amplitude is (sound)_______________ or (light)_________________ 6. Crest: 7. Trough: 8. Condensation: 9.Rarefaction: 10. Phase: 11.Wavelength: 12. Speed: Reference Table Research Name Symbol Value Speed of light in a vacuum Speed of sound in air at STP Visible light frequency range: red violet

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Equation Variables/ constants Units Can be used to find Vector/scalar T T T T = 1/f f f f v v v v =λ f λ λ λ f f f Graph practice: T = 1/f , T versus f f versus T v =λ f , v constant, λ versus f T f λ f T f Algebra practice: 1. Assume speed of sound in air is constant: a. Calculate wavelength of 20 Hz tone b. Calculate wavelength of 20 kHz tone a.____________________ b.____________________ 2. Assume speed of light in a vacuum is constant: a. Calculate wavelength of red light b. Calculate wavelength of violet light a.____________________ b.____________________ Graphing practice: 1. Sketch a sine curve showing two wavelengths, 2. Sketch a sine curve with label crests and troughs;amplitude,wavelength A = 0.4 m, T = 2.0 secs, f =_____ A A

(m) 1 s 2s

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NAME________________________________ DATE________ Regents Physics Wave Notesheet , Part III Mr. Morgante Definitions: 1. Wave front: 2. Doppler effect: 3. Interference: 4. Superposition: 5. Principle of superposition: 6. Constructive interference: 7. Destructive interference: 8. Antinode: 9. Node: 10.Standing wave: 11. Natural frequency: 12. Resonance: 13. Diffraction: Sketchies:Copy and label the review book sketches for the following phenomena:

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Doppler Effect Constructive and Destructive interference Resonance Diffraction

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Name________________________________ Date_______ Regents Physics Mr. Morgante

Intro to Light Notesheet Complete the concept web Law of Reflection Wavefront example Ray example

Visible light , , , , ,

Velocity in a vacuum c =

Frequency range and color f= ____________________ color=_________________

Part of the ______________ spectrum

v = ____ c = ____

Type of wave:______

Wavelength range and color: λ = _______________ color=_____________

Located between ______and _____

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Name:_______________ Date:____________ Regents Physics Mr. Morgante

Constructive and Destructive Interference (Nodal & Antinodal Lines)

On the next sheet you will see S1 & S2 which are two (sources) points in phase. Solid lines are crests, dashed lines are troughs. Make a green dot/circle for all the points where a trough and a crest meet on the diagram. These points are nodal points (where destructive interference occurs). Make a red dot/circle for all the points where a crest and a crest and a trough and a trough meet on the diagram. These points are antinodal points (where constructive interference occurs).

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Name:______________________ Date:________ Regents Physics Mr. Morgante

Wave Multiple Choice Worksheet Question 1

-5

0

5

0 3 6 9 12 15 18 21 24 27 30 33 36

cm

cm

1. The picture above shows a segment of a string along which a transverse wave is moving.

Based on this picture what is the a. amplitude of the wave? b. wavelength of the wave?

Question 2

2. The picture above shows a segment of a string along which a transverse wave is moving.

Based on the picture, what is a. the wavelength of this wave b. the amplitude of this wave?

0 3 6 9 12 15 18 21 24 27 30 33 36

54321

12345

cm

cm

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Question 3

3. The picture above shows a segment of a string along which a transverse wave is moving. Based on this picture, what is a. the wavelength of this wave? b. the amplitude of this wave?

Notice that since there is no scale on this diagram, you will have to use a ruler to measure the

relevant dimensions.

4. What is the frequency of a wave whose period is 0.35 seconds?

5. A boy sitting in a rowboat dips his finger into the water 3 times each second. This creates circular ripples that spread out and hit some nearby rocks. What is the time interval between two successive ripples hitting the rocks?

6. The wind is making the branch of a tree along the shore of a lake dip into the water once every 0.18 seconds. How many circular ripples are created each second?

7. What is the speed of a wave with a wavelength of 0.27 meters and a frequency of 7.5 Hz?

8. A transverse wave is moving along a string. What is the period of this wave if it has a wavelength of 0.45 meters and a propagation speed of 22 m/s?

A woman is fishing from a stationary rowboat in the middle of a lake. A speedboat starting up 7.5 meters away from the rowboat sends out waves with a wavelength of 0.85 meters and a frequency of 0.95 Hz How many seconds must elapse after the speedboat starts up before the first of these waves reaches the rowboat?

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Name:________________________ Date:___________ Regents Physics Mr. Morgante

Worksheet #1 – Wave Phenomena

1. In the diagram below, a water wave having a speed of 0.25 meter per second causes a cork to move up and down 4.0 times in 8.0 seconds. What is the wavelength of the wave?

(1 ) 1.0 m (2 ) 2.0 m (3 ) 8.0 m (4 ) .50 m

2. The periodic wave in the diagram below has a frequency of 40. hertz.

What is the speed of the wave? (1 ) 13 m/s (2 ) 27 m/s (3 ) 60 m/s (4 ) 120 m/s

3. The diagram below represents a rope along which two pulses of equal amplitude, A,

approach point P.

When the two pulses meet at P, the vertical displacement of the rope at point P will be (1 ) A (2 ) 2A (3 ) 0 (4 ) A/2

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4. The driver of a car sounds the horn while traveling toward a stationary person. Compared to the sound of the horn heard by the driver, the sound heard by the stationary person has (1 ) lower pitch and shorter wavelength (2 ) lower pitch and longer wavelength (3 ) higher pitch and shorter wavelength (4 ) higher pitch and longer wavelength

5. What is the frequency of a wave if its period is 0.25 second?

(1 ) 1.0 Hz (2 ) 0.25 Hz (3 ) 12 Hz (4 ) 4.0 Hz

6. A periodic wave with a frequency of 10 hertz would have a period of:

(1 ) 1s (2 ) 0.1s (3 ) 10s (4 ) 100s

7. A laser beam does not disperse as it passes through a prism because the laser beam is:

(1 ) Monochromatic (2 ) Polychromatic (3 ) Polarized (4 ) Longitudinal

8. The diagram below represents wave fronts traveling from medium X into medium Y.

All points on any one wave front shown must be (1 ) traveling with the same speed (2 ) traveling in the same medium (3 ) in phase (4 ) superposed

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9. Which diagram best represents light emitted from a coherent light source?

(1 ) (2 )

(3 ) (4 )

10. In the diagram at the right, monochromatic light ( =5.9 x 10-7meter) in air is about to

travel through crown glass, water, and diamond.

In which substance does light travel the slowest? (1 ) air (2 ) diamond (3 ) water (4 ) crown glass

11. Which diagram below best represents the phenomenon of refraction?

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12. A beam of monochromatic light (f = 5.09 × 1014 hertz) passes through parallel sections of glycerol, medium X, and medium Y as shown in the diagram below.

What could medium X and medium Y be?

(1) X could be flint glass and Y could be corn oil. (2) X could be corn oil and Y could be flint glass. (3) X could be water and Y could be glycerol. (4) X could be glycerol and Y could be water.

13. A ray of light traveling in air is incident on an air-water boundary as shown below. On the paper diagram below, draw the path of the ray in the water.

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Name:___________________ Date:______________ Regents Physics Refraction/Reflection Mr. Morgante 1. Measure the angle of incidence (theta i). Measure the angle of refraction of light IN the medium (theta r)

2a) Label the reflected ray and the refracted ray

2b) What is wrong with this picture below? (hint: measure angles)

Outside Medium - Air Inside medium - Lucite

3. The tallest person that can see her whole body in a .4 meter mirror is _____________ Draw a picture

4. Light starts in medium x (top) and enters water (bottom) at an angle of 20 degrees. The angle of refraction is 40 degrees. What is the index of refraction of medium x. Draw a picture showing how light would bend as goes from medium x to water.

5. What kind of reflection produces an image? __________

6. What kind of reflection doesn’t produce an image? __________________ Why?

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7. Measure the angle of incidence ______ and the angle of reflection. ______ (hint: draw normal first)

8. In refraction, if the angle of refraction is smaller than the angle of incidence, what does that tell you about the speed and index of refraction of the second medium? faster? slower? same?

a. if the angle of refraction is greater than angle of incidence? - second medium is faster? slower? same?

b. if the angle of refraction = angle of incidence? - second medium is faster? slower? same?

9. What is the speed of light in Lucite? (see reference table for equation) ______________

10. Which medium on your reference table is the slowest? ______________ How do you know?

fastest? ______________ How do you know?

11. What if light in a slow medium, bordering on air, comes in at an angle greater than its critical? Draw a picture.

Equal to its critical angle? Draw a picture.

12. What angle of incidence between 2 media never produces refraction ? _____ Draw.

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Name:___________________ Date:______________ Regents Physics Refraction/Reflection #2 Mr. Morgante

1. List 4 reasons why we believe light has a wave behavior (DDIP)

2. How far can light travel in a vacuum for 20 seconds?

3. Name the 6 colors of the spectrum in order.

4. Which color has the largest frequency_____________, smallest frequency ___________, (see reference)

largest wavelength _____________, and smallest wavelength ___________?

5. a) Which color is the fastest in glass? ____________ b) Slowest? _______

6. a) If light comes from air and enters glass, which color is bent the most? ___________

b) The least?______________________

7. What kind of reflection produces an image? __________

8. What color of light has a frequency of 6 x 10 14 Hz? _______________

9. What kind of light did Thomas Young use in his famous double slit experiment? _______

10. Because light can be polarized it proves that light is a _______________ wave.

11. How does the color of a fast moving star change when it turns and comes toward the earth?

_______________ Away from the earth? _____________________

12. a) Do the dangerous electromagnetic waves tend to have a high or low frequency? b) Name two dangerous electromagnetic radiations. _____________ ______________

12 c) All electromagnetic radiations have the same ____________ in a vacuum. 12 d) Electromagnetic radiation is created by accelerating ____________. 13. Where will a ray of light go when it passes from air to glass? ( see picture below) A B C D

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13 a) Which wave characteristics change when light is refracted? direction?___wavelength?___frequency? ___ period? ___ speed? ___

14. A ray of light (A) in Lucite intersects a boundary with air.

a) Which ray shows the path of reflection? ____

b) Which ray(s) are not possible? ____

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15. Which incident ray, if any, is correct? A B C D

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16. Name the wave behavior. Wave Behavior

a)

______________

b)

______________ ______________

c)

_______________________

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17. What do each of the following pictures show? a)

______________ reflection

b)

______________

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c)

______________

d)

___________ ____________ ____________

e)

______________ ______________

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Refraction Practice Problems Part A 1. If light travels through a liquid at 2.50 x 108 m/s, what is the index of refraction (n) of that liquid? 2. What is the speed of light in a substance that has an index of refraction of 2.42? What is that substance? 3. How much does the speed of light slow down as it passes from air into zircon? Part B 4. What is the angle of refraction when light passes from air into diamond at an angle of incidence of 60.0°? 5. Light passes from air into another substance that has an index of refraction of 1.30. If the angle of refraction is 45°, then what is the angle of incidence? 6. If the angle of refraction of a substance is 40.0° and the angle of incidence is 50.0°, what is the index of refraction?

Indices of Refraction Substance Index (n) vacuum air water ethyl alcohol fused quartz glycerine Plexiglas crown glass sodium chloride crystal glass ruby flint glass zircon diamond

1.0000 1.0003 1.33 1.36 1.46 1.47 1.51 1.52 1.53 1.54 1.54 1.65 1.92 2.42

7. A ray of light is incident at an angle of 60 degrees upon the surface of a piece of crown glass (n=1.52).

What is the angle of refraction?

8. Light goes from flint glass (n-1.61) into ethanol (n=1.36). The angle of refraction in the ethanol is 25

degrees. What is the angle of incidence in the glass?

9. A sheet of plastic (n=1.5) is used as the side of an aquarium tank. Light reflected from a fish in the

water has an angle of incidence of 35 degrees. At what angle does the light enter the air?

10. A block of unknown material is submerged in water. Light in the water is incident on the block at an

angle of 31 degrees. The angle of refraction in the block is 27 degrees. What is the index of refraction of

the unknown material?

11. Find the critical angle for diamond (n=2.42)?

12. A block of glass has a critical angle of 45 degrees. Find the index of refraction.