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Total Internal Reflection, Dispersion,

Polarization

• section 26-8

Physics 1161: Lecture 18Total Internal Reflection

normal

θ2

θ1

n2

n1

Recall Snell’s Law: n1 sin(θ1)= n2 sin(θ2)

(n1 > n2 ⇒ θ2 > θ1 )

θ1 = sin-1(n2/n1) then θ2 = 90

θc

θi

θr

“critical angle”

Can the person standing on the edge of the pool be prevented from seeing the light by

total internal reflection ?

1) Yes 2) No

Preflight 18.1

10

58% 42% 8

Indices of Refraction

What is the critical angle of a

diamond-air boundary?1 2

1

sinc

n

nθ − =

Internal Reflection in Diamond

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The diagrams show incident rays approaching a

boundary with a second medium. The relative indices

of refraction of the two media are indicated. In which

diagram will total internal reflection occur, providing

the angle of incidence exceeds the critical angle?

1 2 3 4

0% 0%0%0%

1. Diagram A

2. Diagram B

3. Diagram C

4. None of these

Fiber Optics

Dispersion

prism

White light

Blue light gets deflected

more

nblue > nred

The index of refraction n depends on color!

In glass: nblue = 1.53 nred = 1.52

23

Skier sees blue coming up from the

bottom (1), and red coming down from

the top (2) of the rainbow.

Rainbow: Preflight 18.5

Which is red?

Which is blue?

Blue light is deflected more!

Alexander’s Dark Band

• Sky is light inside primary

rainbow

• Dark between primary

and secondary bows

• Light beyond the

secondary rainbow

• Dark region between is

called Alexander’s Dark

Band

22o Halo

• A halo is a ring of light surrounding the sun or moon.

• Most halos appear as bright white rings but in some instances, the dispersion of light as it passes through ice crystals found in upper level cirrus clouds can cause a halo to have color.

Randomly oriented hexagonal ice crystals

Diameter less than 20.5 micrometers

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Sundogs

• Sundogs or parhelia

on right and left of

sun

Flat faces horizontally oriented

Hexagonal ice crystals

Diameter greater than 30 micrometers

Polarization

• Transverse waves have a polarization

– (Direction of oscillation of E field for light)

• Types of Polarization

– Linear (Direction of E is constant)

– Circular (Direction of E rotates with time)**

– Unpolarized (Direction of E changes randomly)

x

y

Linear Polarizers

• Linear Polarizers absorb all electric fields

perpendicular to their transmission axis.

Molecular View (link)

http://www.colorado.edu/physics/2000/index.pl?Page=polarization/blocking_light.html

Unpolarized Light on

Linear Polarizer

• Most light comes from electrons accelerating in random

directions and is unpolarized.

• Averaging over all directions: Stransmitted= ½ Sincident

Always true for unpolarized light!

Polarizing sunglasses are often considered to be better than tinted glasses because

they…

Preflight 18.3, 18.4

• block more light

• block more glare

• are safer for your eyes

• are cheaper

21

27%

62%

9%

1%

Polarizing sunglasses (when worn by someone standing up) work by absorbing light

polarized in which direction?

• horizontal

• vertical

60%

40%

Brewster’s angleReflected light is partially polarized (more horizontal than vertical). But…

horiz. and vert.

polarized

θB θB

90º-θB

90º

horiz.

polarized

only!n1

n2