Reflection and Refraction of Light: Understanding Polarization

1. Physics 212 Lecture 25

2. Music • Who is the Artist? • The Band • Bob Seger • CCR • Eagles • Steve Miller Band We’ve had a few CCR requests Physics 212 Lecture 24

3. Your Comments “I thought the prelecture was pretty straight forward (minus the slide about intensity - uuuhhh a little more explanation por favor!), but then, the checkpoints were a bit trickier than I expected. Could we go over them please????” Checkpoints – coming up! “Finally! Stuff I actually like and understand!” “Probably the easiest thing we will ever learn all year.” “I didn’t really understand the polarized portion, partially because the prelecture slide was 3 minutes of a non moving picture which surely cannot hold my attention when I’m on a computer. ” We’ll go over the key steps I grow bored of these small time demos. Show us what a well funded, passionate physics professor can do. Why reflected light is polarized; what do electrons have to do with reflected light? “I am confused about the polarization. Why is the horizontal polarization unchanged while the vertical polarization is decreased from incidence to reflected ray??” Brewster's angle really bruised my chances of completely understanding a prelecture ;) the swimming pool question is interesting:) “I could use a little more discussion on the polarization due to reflection.” obviously, the checkpoints • Hour Exam 3: 1 week from tomorrow (Wed. Apr. 25) • covers L19-26 inclusive (LC circuits to lenses) • Sign up for conflicts, etc. no later than Mon. Apr. 23 at 10:00 p.m. 05

4. Let’s start with a summary: from n1 to n2 from n1 to n2

5. since e0 < e The speed of light in a medium is slower than in empty space: vmedium = c / nmedium Remember: k is dielectric constant (capacitors)

6. A ray of light passes from air into water with an angle of incidence of 30 degrees. Checkpoint 1a Which of the following quantities does not change as the light enters the water? A. wavelength B. frequency C. speed of propagation “frequency depends on speed, which obviously changes” “frequency doesn’t depend on the medium. Frequency only depends on the source producing the wave” “Speed of light is always the same.”

7. Observers in both media must agree on the frequency of vibration of the molecules A ray of light passes from air into water with an angle of incidence of 30 degrees. Checkpoint 1a Which of the following quantities does not change as the light enters the water? A. wavelength B. frequency C. speed of propagation What about the wave must be the same on either side ???

8. Reflection

9. Refraction: Snell’s Law

10. This one is better Not the quickest route… Think of a day at the beach… What's the fastest path to the ball knowingyou can run faster than you can swim?

11. Time from A to B : To find minimum time, differentiate t wrt x1 and set = 0 How is x2 related to x1? v = c/n x1 A l1 y1 Same Principle works for Light !! D y2 l2 x2 B Setting dt/dx1 = 0

12. The path of light is bent as it passes from medium 1 to medium 2. Checkpoint 2a Compare the indices of refraction in the two media. A. n1 > n2B. n1 = n2 C. n1 < n2 “by snell’slaw, n1 has to be bigger than n2 to make up for smaller sin(theta1)” “They are the same angles.” “if theta is smaller, n must be smaller”

13. The path of light is bent as it passes from medium 1 to medium 2. Checkpoint 2a Compare the indices of refraction in the two media. A. n1 > n2B. n1 = n2 C. n1 < n2 Snell’s Law: n1sinq1 = n2sinq2 n decreases q increases

14. Total Internal Reflection Total Internal Reflection NOTE: n1 > n2 impliesq2 > q1 BUT:q2has max value = 90o !! q1 > qc

15. A light ray travels in a medium with n1 and completely reflects from the surface of a medium n2. Checkpoint 2b The critical angle depends on: A. n1 only B. n2 only C. both n1 and n2 “n1 determines n2 which determines the critical angle” “Critical angle depends on the incidence angle inside the medium, so only n2 is required.” “n1 must be greater than n2”

16. qc clearly depends on both n2 and n1 A light ray travels in a medium with n1 and completely reflects from the surface of a medium n2. Checkpoint 2b The critical angle depends on: A. n1 only B. n2 only C. both n1 and n2

17. Intensity If two materials have the same nthen its hard to tell them apart. Anything looks like a mirrorif light is just glancing off it.

18. Polarization Snell’s Law: 56.3o

19. A ray of light passes from air into water with an angle of incidence of 30 degrees. Checkpoint 1b 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 “reflection doesn’t polarize previously unpolarized light.” “The vertical component of the E field gets smaller as the ray approaches Brewster&#39;s angle.” “Only vertically polarized light reflects”

20. o = horizontal A ray of light passes from air into water with an angle of incidence of 30 degrees. Checkpoint 1b 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

21. A ball sits in the bottom of an otherwise empty tub at the front of the room. Suppose N people sit high enough to see the ball (N = ).

22. no water qA water qw Snell’s Law: ray bent away from normal going from water to air • A ball sits in the bottom of an otherwise empty tub at the front of the room.Suppose N people sit high enough to see the ball (N = ). • Suppose I fill the tub with water but the ball doesn’t move. • Will more or less people see the ball? • More people will see the ball • Same # will see the ball • Less people will see the ball ??

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. Checkpoint 3 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 “light could all be relected and stay in the water so he can’t see it ” “it depends on the position of the light. if it’s too close to the person, they won&#39;t see it.” “Light comes out at many angles, so while some may be interneally reflected, all cant since they are at differnet angles” “There would be a point where some light would be totally reflected but that would only be for a point, not for the whole light.”

24. 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. Checkpoint 3 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 The light would go out in all directions, so only some of it would be internally reflected. The person would see the light that escaped after being refracted. DRAW SOME RAYS

25. 97º Example: Refraction at water/air interface • Diver’s illusion Diver sees all of horizon refracted into a 97°cone

26. Exercise 45o A meter stick lies at the bottom of arectangular water tank of height 50cm. You look into the tank at an angle of 45o relative to vertical along a line that skims the top edge of the tank. What is the smallest number on the ruler that you can see? nwater = 1.33 50 cm 0 20 40 60 80 100 • Conceptual Analysis: • Light is refracted at the surface of the water • Strategy: • - Determine the angle of refraction in the water and extrapolate this to the bottom of the tank.

27. nairsin(45) = nwatersin(qR) Snell’s Law: sin(qR) = nairsin(45)/nwater = 0.532 qR = sin-1(0.532) = 32.1o Exercise 45o A meter stick lies at the bottom of arectangular water tank of height 50cm. You look into the tank at an angle of 45o relative to vertical along a line that skims the top edge of the tank. What is the smallest number on the ruler that you can see? nwater = 1.33 50 cm 0 20 40 60 80 100 If you shine a laser into the tank at an angle of 45o, what is the refracted angle qR in the water ? A) qR = 28.3o B) qR = 32.1o C) qR = 38.7o

28. qR d d = tan(32.1) x 50cm = 31.4cm Exercise 45o A meter stick lies at the bottom of arectangular water tank of height 50cm. You look into the tank at an angle of 45o relative to vertical along a line that skims the top edge of the tank. What is the smallest number on the ruler that you can see? nwater = 1.33 50 cm 0 20 40 60 80 100 qR= 32.1o What number on the ruler does the laser beam hit ? A) 31.4 cm C) 44.1 cm B) 37.6 cm tan(qR) = d/50

29. Follow-Up 45o A meter stick lies at the bottom of arectangular water tank of height 50cm. You look into the tank at an angle of 45o relative to vertical along a line that skims the top edge of the tank. 50 cm nwater = 1.33 0 20 40 60 80 100 If the tank were half full of water, what number would the laser hit? (When full, it hit at 31.4 cm) E) 44.2 cm C) 32.0 cm B) 31.4 cm D) 40.7 cm A) 25 cm

30. 45o 45o nwater = 1.33 qR 50 cm 50 cm d = 50 cm d = 31.4 cm 0 20 40 60 80 100 0 20 40 60 80 100 qR= 32.1o 45o 50 cm nwater = 1.33 qR d = 40.7 cm 0 20 40 60 80 100 25 cm + (31.4/2) cm

31. More Practice qb Ray exits to air with same angle as it entered !! nsinq is “conserved” A monochromatic ray enters a slab with n1 = 1.5 at an angle qb as shown TOP n = 1 n1 = 1.5 BOTTOM n = 1 qb • Total internal reflection at the top occurs for all angles qb, such that sinqb < 2/3 • Total internal reflection at the top occurs for all angles qb, such that sinqb > 2/3 • There is no angle qb (0 < qb < 90o) such that total internal reflection occurs at top. Snell’s law:

32. Follow-Up q1 n1 Ifn1 = n3 n2 n3 q1 n3 < n1 A ray of light moves through a medium with index of refraction n1 and is incident upon a second material (n2) at angle q1 as shown. This ray is then totally reflected at the interface with a third material (n3). Which statement must be true? q1 n1 (A) (B) (C) n2 n3 Want larger angle of refraction in n3