RefractionThe bending of light due to a change

in speed

Index of Refraction• The index of refraction of a material is the

ratio of the speed of light in a vacuum to the speed of light in the material:

vcn

material in thelight of Speedin vacuumlight of Speed

26.1 The Index of Refraction

Why does light bend?

When light travels from a less optically dense medium to a more optically dense medium, the velocity of the wave decreases. This causes the wave fronts to bunch up and the wavelength then decreases . However, the frequency of the wave remains constant.When the light meets the boundary at an angle, part of the wave front slows down while the other part is still moving quickly. This causes the light to bend.

SNELL’S LAW OF REFRACTION

When light travels from a material withone index of refraction to a material witha different index of refraction, the angleof incidence is related to the angle ofrefraction by

2211 sinsin nn

SNELL’S LAW

26.2 Snell’s Law and the Refraction of Light

Conceptual Example 4 On the Inside Looking Out

A swimmer is under water and looking up at the surface. Someoneholds a coin in the air, directly above the swimmer’s eyes. To theswimmer, the coin appears to be at a certain height above the water. Is the apparent height of the coin greater, less than, or the same as its actual height?

Real World Physics Problems

26.3 Total Internal Reflection

When light passes from a medium of larger refractive index into oneof smaller refractive index, the refracted ray bends away from the normal.

Critical angle 211

2 sin nnnn

c

http://interactagram.com/physics/optics/refraction/

Conceptual Example 6 The Sparkle of a Diamond

The diamond is famous for its sparkle because the light coming fromit glitters as the diamond is moved about. Why does a diamond exhibit such brilliance? Why does it lose much of its brilliance whenplaced under water?

Total Internal Reflection

The Dispersion of Light: Prisms and Rainbows

The net effect of a prism is to change the direction of a light ray.

Light rays corresponding to different colors bend by different amounts.

Thin Films

When light hits a boundary some is reflected and some is refracted

When there are 2 boundaries this happens twice

The two waves in the first medium now interfere with each other. That interference can be constructive if the two waves are

a whole # of wavelengths difference. The interference is destructive if the 2 waves are ½ # of wavelengths different.

The difference is dependent on the thickness of medium B, (the thin film) and the indices of refraction of the materials.

A

B

C

When light goes from a small n to a large n (incident upon a more optically dense medium),

reflection occurs with a phase change of ½ λ. * Think rope with a fixed end reflects back on

opposite side.

When light travels from a large n to a small n there is no phase change. *Think rope with a free end reflects back on the same side.

12

Ray 2 has to travel a longer distance than ray 1. The difference in the distance ray1 travels and ray 2 travels is 2X the thickness of medium B.

If the difference in ray 1 and ray 2 is a whole # of wavelengths constructive interference occurs. Because different colors have different wavelengths. As the thickness of the film varies different colors will constructively interfere and become visible, while other wavelengths of light will destructively interference and disappear. This is what produces the colors seen in a soap bubble or an oil film on a puddle.

Air n=1

n=1.4

Water n=1.33

1

2

t

What is the difference between ray 1 and ray 2?

Both experience a half wavelength phase change at the boundaries. So phase change is not significant.

*Check n change at each boundary.

Air n=1

n=1.4

Water n=1.33

1

2

t

Ray 2 has to travel 2x the thickness of the middle layer

When 2t =1λ, 2λ, 3λ (λ in film) constructive interference occurs.When 2t =1/2λ, 3/2λ, 5/2λ destructive interference occurs.

To find λ in film n1/n2=λ1/λ2

Air n=1

n=1.4

Water n=1.33

1

2

t

Now there is a half wavelength change at only 1 boundary. Which one?

When 1/2 λ + 2t =1λ, 2λ, 3λ (λ in film) constructive interference occurs.

When 1/2 λ + 2t =1/2λ, 3/2λ, 5/2λ destructive interference occurs.