Electromagnetic Waves: NotesLevel 1: Characteristics of Electromagnetic WavesA Review of Waves in General

BIG IDEA 6: Waves can transfer energy and momentum from one location to another without the permanent transfer of mass and serve as a mathematical model for the description of other phenomena.

6.A.1.2: The student is able to describe representations of transverse and longitudinal waves. [SP 1.2]

Waves disturbances that travel through space transferring energy from one place to another.

Sound, light, and the ocean's surf are all examples of waves.

There are two key types of waves: mechanical (made of physical things, like water, sound, the earth…) and electromagnetic (light, x rays…).

Mechanical waves travel through a medium. The medium is whatever is being disturbed by the wave. In the case of a mechanical wave, a physical substace is being “waved”- water washes, jello jiggles…If we are talking about a water wave, water is the medium. It’s important to note that the actual pieces of the medium don’t actually move with the wave. Think of The Wave in a stadium. The particles of the medium (people) move up and down. They don’t actual stay with the moving wave.

That waves carry energy should be obvious. Picture the waves on the ocean. Waves are generated far out at sea mainly by the wind. The wave travels through the water for hundreds or even thousands of miles. Finally, it reaches the shore where the waves pound against the beach. They have enough energy to break down the coastline and erode away continents.

Types of WavesA pulse is one single short wave.

A continuous wave keeps “waving”. There are two types of mechanical waves, the transverse wave and the longitudinal wave.

Transverse Wave - The disturbance direction is perpendicular to the wave direction

Longitudinal Wave - The disturbance direction is parallel to the wave direction

There is also a third, less commonly discussed wave, called a circular wave. In circular waves, the particles move in a circle (go figure).

Take a moment to check out the animations that show each of these waves. It will really help clarify it for you.

Parts of a WaveYou are already familiar with some of these. Wavelength, frequency, amplitude…all of these terms make an appearance again here. Take a look at the wavelength in a longitudinal wave.

You’ve already dealt with frequency, but here is another way of thinking about it.

D ist ur bance d ir ect ion

Wave directionTransver se Wave

L ongitudinal Wave

D ist ur bance d ir ect ion

Wave direction

The frequency of a traveling wave is simply the number of cycles divided by the time they occur in.

Here f is the frequency, n is the number of cycles (and has no unit) and t is the time.

Practice ProblemA speed boat zooms by you as you lie on your floating mattress. You find yourself bobbing up and own on the waves that the boat made. So, you decide to do a little physics experiment. You count the waves and time how long it takes for them to go past. Six wave crests go by in five seconds. So what is the frequency?

Solution

Graphing WavesBelow is the plot of a transverse wave. The displacement is plotted on the y axis and distance is plotted on the x axis. The amplitude, A, is shown. This is the maximum displacement, just as it was for periodic motion. The other thing that is shown on the graph is the wavelength - . The wavelength is the distance between two in phase points on the wave.

Electromagnetic Waves6.A.2.2: The student is able to contrast mechanical and electromagnetic waves in terms of the need for a medium in wave propagation. [SP 6.4, 7.2]

Light is a wave, too. It is an electromagnetic wave (we’ll see why it is called this shortly). Electromagnetic waves encompass a broad range of energy traveling from one place to another- colors, heat, radiation… In the case of electromagnetic waves, there is no medium. An electromagnetic wave can move easily through space, where there is nothing to transfer it- no gas, no water... This baffled scientist for a long time- what is waving? Is there some hidden material out there, wiggling? How does sunlight (a type of electromagnetic wave) get from Point A to Point B?

Electromagnetic waves are transverse waves. We have a changing electric field that has a spatial orientation that is ninety degrees from a changing magnetic wave. Here is a rough drawing of the thing.

Y

X

A

The Electromagnetic Spectrum6.F.1.1: The student is able to make qualitative comparisons of the wavelengths of types of electromagnetic radiation. [SP 6.4, 7.2]

The electromagnetic spectrum encompasses all the various types of electromagnetic waves. The sorting of these waves into specific groupings is, with the exception of visible light, arbitrary. Anyhow, the spectrum is the width and breadth of all the electromagnetic waves. These waves are all the same – a changing magnetic and electric field, but as the frequency varies, the energy changes and this changes the way that they interact with the universe. The spectrum has been arbitrarily chopped up into named groups of waves that have similar characteristics.

Figure 1-http://en.wikipedia.org/wiki/File:EM_Spectrum_Properties_edit.svg

E

B

c

You will not be expected to remember frequencies or wavelengths for these waves. What you will be expected to know is the relative positions of the different types of waves. You should also be cognizant of the fact that the greater the frequency, the greater the energy carried by a light photon (remember E = hf). Thus the greatest energy photons are gamma rays. Also notice that as the frequency gets bigger, the wavelength gets smaller. You do need to memorize the wavelength minimum and maximum for visible light; 400 nm to 700 nm.

You also need to be able to arrange visible light in order of increasing frequency and energy: ROYGBIV.

Gamma rays have the smallest wavelengths and radio waves have the longest.

Since light is a wave, we know that its speed must be equal to its frequency multiplied by its wavelength. In other words:

Here are the different types of waves with a general description of their uses and characteristics.

Radio WavesRadio waves were discovered in 1888 by Hertz. It didn’t take long to come up with a practical use for them – radio! Today radio waves are used for, well, radio – AM radio and short-wave radio both use radio waves. Other communication systems use them as well - cordless telephones, radio controlled toys, cab radios, etc.

MicrowavesMicrowaves were discovered in the early 1900’s. Microwaves are used for FM radio, broadcast TV, radar, cooking food, telephone communication systems, and numerous other communications systems (different types of radio). The cooking food thing is interesting. It turns out that microwaves excite molecules that are about the size of the ones that make up water. Thus, anything that contains a significant amount of water can be heated by microwaves.

InfraredInfrared electromagnetic waves are radiant heat. They are often times referred to as IR. We get a great deal of energy from the sun in the form of infrared waves. When you go out on the first warm spring day and bask in the sun, absorbing all that wonderful heat, you are taking in infrared electromagnetic waves. The wavelength of IR is just right to penetrate your outer skin and excite the molecules in your epidermis, thus heating you up.

VisibleVisible light is important to humans because, you know, most of us see. We arbitrarily arrange light into colors. The main colors, when we think of colors, are red, orange, yellow, green, blue, and violet. The colors are listed in increasing order of frequency. Red light photons have less energy than blue light photons. Commit to memory the energy order of visible light. In order of increasing energy: red, orange, yellow, green, blue, and violet.

The colors correspond to different frequencies (wavelengths) of light. The wavelength of red photons begins at 700 nm (700 x 10-9 m or 7 x 10-7 m). The highest energy violet light photons have a wavelength of 400 nm (4 x 10-7 m).

Ultraviolet LightUltraviolet light or UV is the general group of electromagnetic waves that follows directly after visible light. We can’t see UV, but other critters can. Insect eyes can pick up UV. It turns out that many plain looking flowers reflect lovely patterns when viewed in the UV – no doubt to attract the esthetic senses of discriminating insects. It is easy to see pollen in ultraviolet. The picture below shows a flower in the visible spectrum on the left. On the right, it shows the same flower in ultraviolet.

UV represents the part of the spectrum where the photons have enough energy to be harmful to earthling hominid types. Besides the IR and visible light the sun radiates, it also radiates UV. Fortunately for us, most of this UV is absorbed high in the atmosphere by the ozone layer (ozone is a fancy oxygen molecule that has three oxygen atoms bonded together, O3). But some of it gets through. When you go out and expose your outer surface to the sunlight, the UV, especially the shorter wavelengths, has enough energy to damage skin cells. We call this damage sunburn. Have you ever gotten a bad case of sunburn?

Sunburn is damaging. The skin ages and gets premature wrinkles. Even worse, too much sun has been linked to skin cancer. People can die from skin cancer.

X-RaysX-rays are very high-energy waves that are produced by the decay of unstable radioactive elements or by exciting elements with high voltages. X-rays have a lot more energy than UV. They have so much energy that they can pass right through a person’s soft tissue, but the bones and denser organs absorb them. This is how x-rays at the doctor's office work. A large piece of unexposed photographic film in a protective wrapper is placed on a table. Then the part of the body the doctor is interested in examining is placed on top of the film. x -rays are then zapped into the area. They travel through the soft tissue and expose the film (they affect it just as visible light would). The bones absorb the x-rays so that the film under the bones is not exposed. The film is developed and a picture of the interior of the body is revealed - shadows where the bones blocked the x-rays.

X-rays have a great deal of energy, so doctors are very careful to prescribe them only when they are really needed. Over exposure to x-rays is very dangerous. The x-rays penetrate the body and have collisions with atoms in the various tissues. They can knock atoms loose and break chemical bonds. When they mess up DNA molecules a body can end up with mutations. One can also get a really bad form of skin cancer called melanoma.

Gamma RaysAbove the x -rays are the gamma rays (-rays). -rays are also produced by the decay of radioactive elements. They are the most energetic of all the electromagnetic waves and can be enormously destructive. They have tremendous penetrating power. Gammas are produced naturally in the earth and atmosphere by the decay of radioactive elements. We also get a lot of them from space – they are one of the constituents of what we call “cosmic rays”. So we are exposed to them all the time - they are part of what is called the earth’s background radiation. It is a most fortunate fact that our bodies can deal with the damage caused by this form of radiation. Exposure to artificial -rays above the natural background, however, is extremely dangerous. People whose work could expose them to such radioactivity have strict limits on the amount of exposure they are allowed. Their exposure is monitored with personal film badges as well as installed radiation detectors.

Vision Words to KnowLuminous: Gives off light

Transparent: You can see through the object completely

Translucent: You can see through it partially (such as a fogged glass window in a bathroom)

Light as a RayOne of the most important ideas to remember is we conceptualize light as a ray- a straight line. When we draw the path of light, we use a straight line that will continue, unchanged, until it interacts with a different matter. You will see lots of examples of this in the following section.

Level 2: Reflection and Refraction6.E.2.1: The student is able to make predictions about the locations of object and image relative to the location of a reflecting surface. The prediction should be based on the model of specular reflection with all angles measured relative to the normal to the surface. [SP 6.4, 7.2]

How Light Interacts with LightLaw of Reflectionfrom REA Notes

Practice Problem: Law of Reflection

Introduction to Refraction6.E.1.1: The student is able to make claims using connections across concepts about the behavior of light as the wave travels from one medium into another, as some is transmitted, some is reflected, and some is absorbed. [SP 6.4, 7.2]

So far we’ve talked about what happens when light bounces off a reflective surface. What happens when light hits a surface and isn’t completely reflected?

First, some vocabulary. The surface of the material is called the surface boundary. This can be anything- a plane of glass, a table top, even the curve of water droplet. Imagine a perpendicular line that comes straight up from the boundary. We call this the normal line. Remember the normal force when you

learned friction? This points in the same direction. The normal line always sticks straight out of the surface, even if the surface is curved. The picture on the right shows the normal lines at different points on a curved surface. This will become important later.

The light that hits the material is called the incident beam. The medium this light was traveling through originally is called the incident medium. If light travels through the air and hits glass, air is the incident medium.

Once it hits the medium, a few things happen. The wave splits up. Part of it will be reflected. Part of the wave will be transmitted. And some of the energy will be absorbed. How much is absorbed, reflected and absorbed depends on the material. Some materials (like glass) transmit a lot. Other materials (like dark murky water) do not transmit as much.

The part of that gets reflected follows the law of reflection (see section above). The light that is absorbed will slightly heat the material (and later come off as infrared radiation). What happens to the part that is transmitted into the medium? In this section, we are going to focus on what happens to the transmitted beam of light.

When light moves from one medium to another, its speed changes. A measure of how slow or fast light is going in a medium is the index of refraction (see the chart on the right). You don’t need to memorize these. Notice, however, that air has an index of refraction that is pretty much 1. For most problems (unless otherwise stated) you can use 1 for air (or other gases, like carbon dioxide). In a vacuum, the index of refraction is 1. You will never have an index of refraction greater than one because this implies light is going faster than the speed of light, which breaks physics. The higher the index of refraction, the slower light will go in the medium. Here’s an equation that expresses this idea:

To calculate the index of refraction, we can use:

n= cv

Practice Problem: Super EasyWhat is the speed of light in ice?

SolutionWe use the index of refraction equation to find the speed in the ice.

Snell’s Law6.E.3.1: The student is able to describe models of light traveling across a boundary from one transparent material to another when the speed of propagation changes, causing a change in the path of the light ray at the boundary of the two media. [SP 1.1, 1.4]

6.E.3.2: The student is able to plan data collection strategies as well as perform data analysis and evaluation of the evidence for finding the relationship between the angle of incidence and the angle of refraction for light crossing boundaries from one transparent material to another (Snell’s law). [SP 4.1, 5.1, 5.2, 5.3]

6.E.3.3: The student is able to make claims and predictions about path changes for light traveling across a boundary from one transparent material to another at non-normal angles resulting from changes in the speed of propagation. [SP 6.4, 7.2]

Substance Index of Refraction

Diamond 2.419Fused quartz 1.458Crown glass 1.52Flint glass 1.66Ice 1.309Polystyrene 1.49Benzene 1.501Ethyl alcohol 1.361Water 1.333Air 1.000 293Carbon dioxide 1.000 45

Snell’s Law appears very easy when you first encounter it (and the equation really is). However, there are lots of tricky ways to force students to apply it. It can get very complicated and very heavy on the trig. You need to have Snell’s Law down cold. I have put a series of practice problems below, in order of increasing difficulty. You should try each problem first and then check the solution. Certain doom awaits those who do not.

Now that we are familiar with the index of refraction, we can use it to calculate the angle of refraction. To do this, we use a super useful equation called Snell’s Law.

n1 sin θ1=n2sin θ2Use the picture above to help you organize the variables above. Then try the example problems below. Keep in mind that the angle is from the normal, not the surface. They will try to trip you up on that.

Snell’s Law is a mathematical way of saying something that can (and should) also be understood more generally. When light travels from a less dense medium to a more dense medium, its angle to the normal decreases. When it travels from a more dense medium to a less dense medium, its angle to normal increases. I’ve always kept track of this by thinking of the angle getting squeezed in dense material and it relaxes and spreads out in a less dense material. This is just a memory trick- not actual physics.

Practice Problem: Try Snell’s LawA beam of light that has a wavelength of 651 nm traveling in air is incident on a slab of transparent material. The angle of incidence is 35.0. The angle of refraction is 23.4. Find index of refraction for slab.

Solution

For all practical purposes, the index of refraction in air is 1.

n1

1

n2

2

su bsta n c e 1

su bsta n c e 2

Practice Problem: Drawing the Diagram

AP Level Practice Problem:

Solution

AP Practice ProblemThis is a typical type of Snell’s Law AP Free Response question.

Solution

Level 3: Critical Angle and Wavelengths in New MediumsCritical Angle

When we send light from a more dense material into a less dense material, something interesting happens. As the angle of incidence on the surface increases, the angle of refraction increases. Because you are going from more dense to less dense, the angle of refraction is larger by some factor than the angle of incidence (that factor is determined by the difference in the index of refractions). At some point, the refracted angle will actually equal 90 degrees. The light will no longer leave the

substance- it will essentially move along the surface at this angle. We call this angle- the maximum angle where light is still refracted- the critical angle.

It is very easy to calculate and you already know the equation to do it. Just use Snell’s law, and enter 90 degrees for the refracted angle (because the light is now refracted at 90 degrees).

Practice Problem: Critical Angle Practice

AP Practice: Extending the Fisherman ProblemThis is a very typical type of Snell’s AP Free Response. It would build off of the previous fisherman question (as it does here). Make sure you solve this before looking at the solutions.

Solution

Total Internal ReflectionWhat happens if then we go past the critical angle? Well, then the light will actual reflect back into the material. We call this total internal reflection. In other words, none of the light is escaping the material at this point- it will all be reflected back into the material. From then on, you can use the law of reflection.

Keep in mind that total internal refraction can only occur when we go from a more dense medium to a less dense medium.

See the reflection of the turtle above? Total Internal Refraction causes this.

This is actually how fiber optic cables work (see below).

AP Like Practice Problem:

Solution

Supplemental: Planet Earth: Cave Diving in Haloclines One of the most stunning examples of how the index of refraction can mess with your mind.

Wavelength and Frequency in a New MediumThe direction of the beam of light isn’t the only thing that changes when it enters a new medium. The speed of the wave and the wavelength change as well. We are going to do some calculations with this idea, but before we do you need to hammer one key idea into your mind before we move on- the frequency of the wavelength will not change in the new medium. That is already set- you can’t make a light wave go back in time and unwiggle itself (this is terrible scientific thinking, I

apologize) any more than you can make a slinky wave go back and time and unwiggle itself. It already has that energy, so it already has that set frequency.

Knapp’s notes will walk us through a practice problem below.

Practice ProblemA Beam of light with a wavelength of 565 nm is traveling in air and is incident on slab of transparent material. The angle of incidence is 32.0. The refracted beam makes an angle of 20.5. (a) Find the index of refraction for the slab and (b) find the wavelength of the light in the second medium.

Solution

(a)

(b) We know the index of refraction in the second medium. We can use this to find the speed of light in this medium:

Using this and the equation relating wavelength and velocity, we can find the wavelength in the new medium

But what is the frequency? Well we can solve for the frequency of the light in air (recall that the frequency of the light will be the same in both mediums):

Okay, we can plug this into the velocity equation, which we solve for wavelength.

DispersionHere is something you wouldn’t expect- it still messes with my mind sometimes. We just talked about the speed of light in different mediums. Now let’s talk about the speed of color in different mediums. That’s right- you heard me. If we were to send a beam of white light (which is made up of red, yellow, green….) into a medium, we would find that the different colors actually move at different speeds through the same medium. This is called dispersion.

It also kind of goes the opposite of what you would think- lower energy red light actually travels slightly faster than the high energy blue light. We are not going to get into why. But here is what you need to remember: The lower the frequency of light, the faster it will move through any given medium.

This also means that each color really has its own index of refraction. When we make a list of indexes of refractions we are actually creating them based on plain old yellow light. Different colors would move through the same materials would experience them with slightly different index of refractions. Here are the different values for glass.

Notice that violet light has the highest index of refraction. This means that it will be bent quite a bit when it enters glass at an angle. Red, other the other hand, has a slightly lower index of refraction. It will be bent less when it enters a glass at an angle.

I’m going to be honest with you- you won’t need to touch this stuff for 90% of light. But every now and then you will need to. Here is how you know- if there is a prism or a rainbow involved, you will need to care about the different index of refractions for different colors. You will also need to know it to fully appreciate this album cover:

This album cover was caused by dispersion. In fact, it pretty clearly illustrates dispersion right there. The purple light has a higher index of refraction, so, according to Snell’s Law, it experiences the greatest angle of refraction. Ta-da! Rainbows are born.

AP Like Practice Problem: DispersionTry this before you look at the solution… and keep in mind that the light both enters and exits the prism.

Solution

Level 3: Ray Diagrams MirrorsLO 6.E.4.2: The student is able to use quantitative and qualitative representations and models to analyze situations and solve problems about image formation occurring due to the reflection of light from surfaces. [SP 1.4, 2.2]

LO 6.E.4.1: The student is able to plan data collection strategies, and perform data analysis and evaluation of evidence about the formation of images due to reflection of light from curved spherical mirrors. [SP 3.2, 4.1, 5.1, 5.2, 5.3]

Okay, now that we’ve deep into the heart of how light interacts with materials- reflection and refraction- it’s time to take these ideas for a spin and apply them.

Here is the key idea behind this whole section: your brain doesn’t know that light bends or reflects. It believes that light moves in a straight line- from the source to your eye ball. Think about looking in the mirror. Let’s say you have a candle sitting beside you in a dark room. The light leaves the candle, bounces off the mirror and hits your eye. Your brain does not think about this journey when it looks around- it just sees a candle sitting inside the mirror.

As a rule, we use complete lines to show the actual path of the light, and dotted lines to show where you brain would think this light came from. We call these lines back rays because your brain thinks it can trace them back into the mirror. You can see an example of this in the previous picture.

Here is another picture of that same idea. Notice that the brain thinks the light source is actually inside the mirror.

Plane MirrorsA plane mirror is a flat reflective surface- mirror in your bathroom, surface of a lake, anything like that. We’ve already shown several examples of these (above).

Whenever we talk about the type of image any mirror (plane, concave, convex… we’ll talk about these soon), we pretty much ask ourselves the same four questions:

1. Where is the image?2. Is it real or virtual?3. Is the image upright or inverted?4. What is the height of the image?

Let’s use a plane mirror to practice answering these questions.

1. Where is the image?

This talks about where your brain perceives the image to be. Look at the picture. Where does your brain think the object is? You could do a ton of trig to figure this out, but you already know the answer. The brain thinks the image is in the mirror. How far back? The exact distance the object is from the mirror. If you are standing five feet from the mirror, it will look like you are standing five feet inside the mirror- or ten feet away from yourself. We talk about the distance from the mirror, so we would say 5 ft is the distance to the image.

2. Is the image real or virtual?

This is a virtual object. To the eye, it appears to have come from inside the mirror. We will get into this more later. It will be more obvious in the next section.

3. Is the image upright or inverted?

This is easy. Take a look. The object still appears upright.

4. What is the height of the object?

Easy. It appears the same inside the mirror.

Types of MirrorsOkay, now we are going to have some fun. And by fun I mean tears. No really, they actually aren’t that bad, but they do take practice. If you don’t practice these as we go, you will soon be hopelessly lost.

Concave mirrors are mirrors are mirrors that curve inward. This is easy to remember- when you are standing in front of them, they look like caves (shape wise- not what you actually see in the mirror). Convex mirrors look like they bubble out toward you.

Think of a spoon. Think specifically about the part that holds the food. If you were to look at that side of the spoon, you are looking at a tiny concave mirror. If you flip it over so that the surface now bubbles out at you- this is a convex mirror. You can see this in the pictures. In both pictures, imagine you are standing on the left side of the mirror.

The law of reflection would still apply to these mirrors, of course. Only now, at any given point, the surface might be tilted slightly. This means the light will reflect at different angles

Parts of a Mirroradapted from Knapp Notes

Figure 2-Concave Mirror

Figure 3-Convex mirror

C is the center of curvature. If the curve of the mirror were to continue until it formed a sphere, C would be at the center of the sphere. Its distance from the center of the mirror is equal to the radius of curvature R for the mirror.

The principle axis is a line that goes through the center of curvature to the center of the mirror.

f is the principle focus. It is also called the focal point or sometimes simply the focus. If you send a ray of parallel ray of light toward a concave mirror, the law of reflection will bend that light toward the focal point.

The focal length is the distance from the principle focus to the center of the mirror. It is equal to one half of the radius.

Rules for Ray DiagramsWhen we are talking about mirrors (or, later on, lenses) we often want to figure out where it would look like an object is (like we did before with the plane mirror). In order to do that, we use a trick of tracing a few key rays of light as they interact with the mirror. We call these ray diagrams. We will get to these in a second, but first we have to know a few things about how a ray of light would interact with a mirror.

If a ray of light is moving parallel to the principle axis and it strikes a concave mirror, the law of reflection tells us that it will be directed toward the focal point. You can see this in the highlighted ray below. We use this idea by imagining a ray of light left the top of the object and headed toward the mirror parallel to the principle axis.

VC

R

Pr inciple axisf

Light that happens to pass through the focal point and then hit the mirror will travel away from the mirror going parallel to the principle axis. We show this in a ray diagram by drawing the highlighted ray below.

Last, if the ray leaves the object and passes through the center of curvature, it will rebound straight back through the center of curvature.

If you draw all three of these lines, you will see that they all cross at one point. Draw the object from the principle axis to this point. This is where the image will be formed.

Cf

123

Cf

123

Cf

123

How are you going to remember to draw all these? Here is what I tell myself to keep these straight:

Flat to focal, focal to flat.

In other words, draw a flat line that hits the mirror and then passes through the focal point. Then draw a line from the focal point that then (after hitting the mirror) is flat.

This will help you remember the first two (which is, actually) all you will really need. The third one is helpful in confirming that you’ve done it right.

Listen to me- the only way to get good at these is to practice. You have to practice and practice and practice. Otherwise, they are insanely easy to mess up. Once you’ve done several, you get a sense for them and they are easy. If you don’t- I promise you, you will soon be completely lost.

Video Example: Watch someone else teach this.

Practice: Drawing a Ray Diagram

Solution

Let’s ask ourselves the key questions about the image formed in this practice question:

1. Where is the image?

The image is in front of the mirror.

2. Is the image real or virtual?

This is a real image. How do we know? Take a look- do you see how the actual solid lines of the ray diagram come together to create the image? That won’t always be the case. In some situations (which we will encounter soon), the back rays are actually the ones that converge. This will be more obvious in a couple of examples.

What you need to know now is that virtual images are what we are used to- what we see in the mirror. Real images are different. You can put a screen at their location and you will actually see the image projected there. Any time you watch a movie in a theater, you are watching a real image.

3. Is the image upright or inverted?

This is easy. Take a look. The image is inverted (upside down)

4. What is the height of the object?

The image is smaller than the real object (see the ray diagam).

Object Inside a Concave Focal PointSomething interesting happens if we move the object so that it is closer to the mirror than the focal point. You can still repeat the mantra of “Flat to focal, focal to flat”. In this situation, however, you will also need to show the back rays. This is actually really hard to describe on paper. It’s a lot easier to follow when you watch someone do it. Keep an eye on the fact that he is using the back rays to figure out where the image is.

Video Example: You must watch this video. Creating a virtual image in a concave mirror.

Okay, in that video, the image created was a virtual image. This means that it was created by back rays coming together. It can’t be projected onto anything- it looks like it exists inside the mirror. Take a look at the difference below. When rays of

light converge (like the picture on the left), we have a real image, which can be projected onto something. When we have back rays coming together (like the one on the right), we get a virtual image.

Stop! Before you move on, complete the Classroom Physics: Ray Diagrams for Concave Mirrors. Take your time and check your work before moving on.

Convex MirrorsNow we get to the type of mirror that bubbles out toward you. This is like the underside of a spoon. When light hits a convex mirror, it gets bent away from the principle axis.

To the outside observer, this makes it appear as though the light is actually being focused to a point inside the mirror. This is called the virtual focal point.

For convex mirrors, we can still use the mantra “Flat to focal, focal to flat,” only now we are going to use the focal point inside the mirror. Again, this is much easier to watch than to learn described on paper.

Video Example: Convex Mirror Ray Diagrams. You must watch this!!!!

Here’s an important thing to keep in mind about convex mirrors. They will always produce images that are:

located behind the convex mirror a virtual image an upright image reduced in size (i.e., smaller than the object)Savor that “always”- we don’t get many “always” in physics, but this is one. It makes answering multiple choice questions about convex mirrors a lot easier. As long as you can keep your wits about you and remember that the image is virtual, upright, and smaller, you can answer questions about the images in

convex mirrors very quickly. In fact, the further we move the object away from the mirror, the smaller the image will become:

Stop! Go work on the Physics Classroom: Convex Mirrors Page now

Level 4: Mirror- Lens Equationfrom Princeton Review

Practice Problem: Mirror Lens Equation

Solution

AP Practice: More Mirror Lens Equation

Solution

Practice: Even More Mirror Lens

Solution

Practice: All the Mirror Lens Equation Practice You Can Handle

Solution