the wave model · 2019-09-17 · light passes from vacuum (index of refraction n = 1) into water...

$: The wave model · 2019-09-17 · Light passes from vacuum (index of refraction n = 1) into water ... A. and the light speeds up as it enters the second medium. B. and the light slows$
© 2017 Pearson Education, Inc. Slide 32-1

Models of Light

The wave model: Under many circumstances, light exhibits the same behavior as material waves. The study of light as a wave is called wave optics.

The ray model: The properties of prisms, mirrors, and lenses are best understood in terms of light rays. The ray model is the basis of ray optics.

The photon model: In the quantum world, light behaves like neither a wave nor a particle. Instead, light consists of photons that have both wave-like and particle-like properties. This is the quantum theory of light.

Waves and wave fronts

• A wave front is the locus of

all adjacent points at which

the phase of a wave is the same.

• Spherical wave fronts of

sound spread out uniformly

in all directions from a point

source.

• Electromagnetic waves in

vacuum also spread out as

shown here.

© 2016 Pearson Education Inc.

Wave fronts and rays

• It’s often convenient to represent a light wave by rays rather

than by wave fronts.

• A ray is an imaginary line along the direction of travel of the

wave.

• When waves travel in a

homogeneous isotropic

material, the rays are

always straight lines

normal to the wave

fronts.


Wave fronts and rays

• Far away from a source, where the radii of the spheres have

become very large, a section of a spherical surface can be

considered as a plane, and we have a plane wave.



Objects can be

either self-luminous,

such as the sun and

lightbulbs, or they

can be reflective.

Most objects are

reflective.

Light from Objects


Rays originate from every point on an object and

travel outward in all directions, but a diagram trying to

show all these rays would be messy and confusing.

To simplify the picture, we use a ray diagram showing

only a few rays.

Ray Diagrams


The law of reflection states that

1. The incident ray and the reflected ray are in the same

plane normal to the surface, and

2. The angle of reflection equals the angle of incidence:

r = i

Reflection


Example 1

A dressing mirror on a closet door is 1.50 m tall. The bottom

is 0.50 m above the floor. A bare lightbulb hangs 1.00 m from

the closet door, 2.50 m above the floor. How long is the streak

of reflected light across the floor?

Diffuse and specular reflection

• Our primary concern in this

chapter will be with specular

reflection from a very smooth

surface such as highly polished

glass or metal (a).

• Scattered reflection from a

rough surface is called diffuse

reflection (b).

• The vast majority of objects in

your environment are visible to

you because they reflect light

in a diffuse manner.



Consider P, a source of rays that reflect from a mirror.

The reflected rays appear to emanate from P′, the same

distance behind the mirror as P is in front of the mirror.

That is, s′ = s

The Plane Mirror


The Plane Mirror


QuickCheck

You are looking at the image of a

pencil in a mirror. What do you see

in the mirror if the top half of the

mirror is covered with a piece of

dark paper?

A. The full image of the

pencil

B. The top half only of the

pencil

C. The bottom half only of

the pencil

D. No pencil, only the paper


Example 2

If your height is h, what is the shortest mirror on the wall in

which you can see your full image? Where must the top of the

mirror be hung?


In-class Activity #1

A light ray leaves point A in the figure, reflects from the mirror,

and reaches point B. How far below the top edge does the ray

strike the mirror?


Two things happen when a light ray is incident on a

smooth boundary between two transparent materials:

1. Part of the light reflects

from the boundary,

obeying the law of

reflection.

2. Part of the light continues

into the second medium.

The transmission of light

from one medium to

another, but with a change

in direction, is called

refraction.

Refraction

Index of refraction

• The index of refraction of an optical material (also called the

refractive index), denoted by n, is defined as:

• For the case shown here, material b has a larger index of

refraction than material a (nb > na) and the angle θb is smaller

than θa.


Reflection and refraction: Case 1 of 3

• When a ray passes from one material into another material

having a larger index of refraction and hence a slower wave

speed, the angle θb with the normal is smaller in the second

material than the angle θa in the first.



• When a ray passes from one material into another material

having a smaller index of refraction and hence a faster wave

speed, the angle θb with the normal is larger in the second

material than the angle θa in the first.



• In the case of normal incidence, the transmitted ray is not

bent at all.

• In this case θa = 0 and sin θa = 0, so θb is also equal to zero;

the transmitted ray is also normal to the interface.

• θr is also equal to zero, so the reflected ray travels back along

the same path as the incident ray.


The law of refraction

• This result is also called Snell’s law, after the Dutch scientist

Willebrord Snell (1591–1626).


Why does the ruler appear to be bent?

• The law of refraction explains why a partially submerged

straight ruler appears bent.

• Light rays coming from below the surface change in direction

at the air–water interface, so the rays appear to be coming

from a position above their actual point of origin.


Why does the ruler appear to be bent?


© 2016 Pearson Education, Inc.

Light passes from vacuum (index of refraction n = 1) into water

(n = 1.333). If the incident angle is an acute angle

QuickCheck

A. the refracted angle is greater than the incident angle.

B. the refracted angle is equal to the incident angle.

C. the refracted angle is less than the incident angle.

D. two of A, B, and C are possible, depending on the specific

value of .

© 2016 Pearson Education, Inc.

Light passes from a medium of index of refraction na into a

second medium of index of refraction nb. The angles of

incidence and refraction are respectively. If na < nb,

QuickCheck

A. and the light speeds up as it enters the second

medium.

B. and the light slows down as it enters the second

medium.

C. and the light speeds up as it enters the second

medium.

D. and the light slows down as it enters the second

medium.


A laser beam passing

from medium 1 to

medium 2 is refracted as

shown. Which is true?

QuickCheck

A. n1 < n2

B. n1 > n2

C. There’s not enough

information to compare

n1 and n2.


Indices of Refraction

When light passes from vacuum (index of refraction n = 1)

into water (n = 1.333),

QuickCheck

A. the wavelength increases and the frequency is unchanged.

B. the wavelength decreases and the frequency is

unchanged.

C. the wavelength is unchanged and the frequency increases.

D. the wavelength is unchanged and the frequency

decreases.

Index of refraction and the wave aspects of light

• The frequency f of a wave does not change when passing

from one material to another.

• In any material, v = λf ; since f is the same in any material as

in vacuum and v is always less than the wave speed c in

vacuum, λ is also correspondingly reduced.

• When a wave passes from one material into a second material

the waves get “squeezed” (the wavelength gets shorter) if the

wave speed decreases and get “stretched” (the wavelength

gets longer) if the wave speed increases.



The figure shows a wave crossing the boundary between two

media, where we’re assuming n2 > n1.

Because the wavelengths differ on opposite sides of the

boundary, the wave fronts can stay lined up only if the waves

in the two media are traveling in different directions.

Refraction


Example 3

In the figure, material a is water and material b is glass with

index of refraction 1.52. The incident ray makes an angle of

60.0º with normal; find the directions of the reflected and

refracted rays.


Example 4

What is the prism’s index of refraction?


Example 5

The wavelength of the red light from a helium-neon laser is

633 nm in air but 474 nm in the aqueous humor inside your

eyeball. Calculate the index of refraction of the aqueous

humor and the speed and frequency of the light in it.


Example 6

Two mirrors are perpendicular to each other as seen in the

figure. A ray traveling in the xy-plane is reflected from one

mirror at P, then the other at Q. What is the ray’s final direction

relative to its original direction?


In-class Activity #2

Find the index of refraction for material X. Also, determine

the angle the light makes with the normal in the air.

the wave model · 2019-09-17 · light passes from vacuum (index of refraction n = 1) into water...

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