# Physics 2112 Unit 25 Topic 25, Slide 1 What happens at boundaries - Reflection - Refraction - Snell’s Law - Critical Angle Polarization - Brewster’s Angle.

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Physics 2112 Unit 25 Topic 25, Slide 1 What happens at boundaries - Reflection - Refraction - Snell’s Law - Critical Angle Polarization - Brewster’s Angle

Recall from 2111: When wave hits a boundary where speed changes - part is transmitted - part is reflectedDEMODEMO Boundaries Topoc 25, Slide 2 Same with E&M: Think of window. Can see through it Can see reflection in it Speed of light is different in vacuum and glass

Relative speeds given by index of refraction, n Speed of Light in media Topic 25, Slide 3 n = speed of light in vacuum speed of light in media Media n vacuum 1.0 air ~1.0 water 1.33 alcohol 1.36 glass 1.5 diamond 2.4 = V C Recall: So can think of n as:

Reflection Topic 25, Slide 4 Measured from normal

CheckPoint 2: Changes at Boundary Topic 25, Slide 5 Which of the following quantities does not change as the light enters the water? A.wavelength B.frequency C.speed of propagation D.(A) and (B) E.(B) and (C) A ray of light passes from air into water with an angle of incidence of 30 degrees. 30 o

Refraction: Snell’s Law Unit 25, Slide 6 D a b c d t ab = t dc t ab =  x ab /v 1

Not the quickest route… This one is better What's the fastest path to the ball knowing you can run faster than you can swim? Think of it another (weird) way… Topic 25, Slide 7 Minimum Travel Time

A B x1x1 y1y1 l1l1 x2x2 y2y2 l2l2 Setting dt/dx 1  0 Same Principle works for Light! D Topic 25, Slide 8 v  c/nv  c/n How is x 2 related to x 1 ? To find minimum time, differentiate t wrt x 1 and set  0 Time from A to B : Not on test….

REALLY(!) weird (….but not on test) This business of “minimum travel time” is everywhere in nature! Remember from 2111? When you kick a soccer ball up at 30 o, where does it land? It lands so that the integral has minimum value. “Principle of Least Action” “Lagranginan”

A ray of light is bent as it passes from medium 1 to medium 2. Compare the indices of refraction in the two mediums. A.n 1 > n 2 B.n 1 = n 2 C.n 1 < n 2 Topic 25, Slide 10 CheckPoint 2: Refraction

How much is the beam shifted by the cube? Example 25.1: Cube of Glass Topic 25, Slide 11 25 o ? A beam of laser light hits a cube of glass that is 4cm on a side with a angle that is 25 o to the normal. The index of refraction for glass is n= 1.5. At what angle will it leave the cube? ?

The light from a fish is incident from below on the boundary between water and air with an incident angle of 30 o. At what refracted angle does it leave the boundary? Example 25.2: Fish in the water Topic 25, Slide 12 What if the incident angle had been 60 o ? 30 o

1  c1  c Total Internal Reflection NOTE: n 1  n 2 implies  2   1 BUT:  2 has max value = 90 o ! Total Internal Reflection Unit 25, Slide 14

Example 25.3: Diver’s Ilusion Unit 25, Slide 15 If a scuba diver looks straight up towards the surface from underwater, he see a bright circle of light. Why? What is the size of that circle?

Checkpoint 2 Electricity & Magnetism Lecture 25, Slide 16 A light ray travels in a medium with n 1 and completely reflects from the surface of a medium with n 2. The critical angle depends on: A.n 1 only B.n 2 only C.both n 1 and n 2

How much is reflected? Unit 25, Slide 17 When going from n 1 >n 2, some is reflected, some is transmitted (refracted) How much goes into each? Complex. We can do extremes.

Example 25.3: Reflection from Window Topic 25, Slide 18 If you looked straight into a window made of regular glass, you would see a reflection of the things behind you. What refraction of the intensity of the original waves would in that reflected image?

Polarization Topic 25, Slide 19 Unpolarized Intensity decreased in plane of incidence Partially polarized plane of incidence

Polarization Unit 25, Slide 20 Snell’s Law: Completely polarized when  1 +  2 = 90 o Brewster’s Angle:  B = tan -1 (n 2 /n 1 )

Example 25.4: Brewster’s Angle Topic 25, Slide 21 A light beam is incident on a piece of glass (n=1.5) at the minimum angle for which to reflected beam is completely polarized. What is  r for the portion of the beam that is refracted? BB rr

CheckPoint 4 Topic 25, Slide 22 Some of the light also reflects off the surface of the water. If the incident light is initially unpolarized, the reflected light will be A.Unpolarized B.Somewhat horizontally polarized C.Somewhat vertically polarized A ray of light passes from air into water with an angle of incidence of 30 degrees. 30 o

CheckPoint 3 Electricity & Magnetism Lecture 25, Slide 23 A light is shining at the bottom of a swimming pool (shown in yellow in the figure). A person is standing at the edge of the pool as shown. Can the person standing on the edge of the pool be prevented from seeing the light by total internal reflection at the water-air surface? A.yes B.no

Dispersion Topic 25, Slide 24 Speed of E&M wave in media decreases in media slightly with frequency n is slight frequency (wavelength) dependent dispersion

Rainbows Topic 25, Slide 25 Mixed (white) light Refraction (dispersion) reflection Refraction (dispersion) Rain drops 84 o

50 cm 200406080100 45 o A meter stick lies at the bottom of a rectangular water tank of height 50cm. You look into the tank at an angle of 45 o relative to vertical along a line that skims the top edge of the tank. n water  1.33 Example 25.4: Meter Stick in Tank Unit 25, Slide 26 What is the smallest number on the meter stick that you can see? meter stick

from n 2 to n 1 Summary Unit 25, Slide 27

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