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# Lect25 - Physics 212 40 30 20 10 0 Confused Avg = 3.0...

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Unformatted text preview: Physics 212 Lecture 25 50 40 30 20 10 0 Confused Avg = 3.0 Confident Physics 212 Lecture 25, Slide 1 Music Who is the Artist? A) B) C) D) E) Miles Davis Oscar Peterson Gerry Mulligan John Coltrane Stan Getz Why? Just in a classic jazz mood, I guess I also was at a concert last Saturday when the also vocalist called Lush Life “obscure” hardly…… Physics 212 Lecture 25, Slide 2 Physics 212 Lecture 25 50 40 30 20 10 0 Confused Avg = 3.0 Confident Physics 212 Lecture 25, Slide 3 Let’s start with a summary: from n2 to n1 Physics 212 Lecture 25, Slide 4 The speed of light in a medium The is slower than in empty space: is since ε0 > ε vmedium = c / nmedium Physics 212 Lecture 25, Slide 5 Preflight 2 BB A B C What about the wave must be the same on either side ??? 60 Observers in both media must agree on the frequency of vibration of the molecules 50 40 30 20 10 0 Physics 212 Lecture 25, Slide 6 Reflection Physics 212 Lecture 25, Slide 7 Refraction: Snell’s Law Physics 212 Lecture 25, Slide 8 Think of a day at the beach… What's the fastest path to the ball knowing you can run faster than you can swim? This one is better Not the quickest route… Physics 212 Lecture 25, Slide 9 A x1 l1 y1 y2 l2 x2 B 1 Time from A to B = t = l1/v1 + l2/v2 = Time v1 dt x1 x2 dx2 = + 2 2 2 2 dx1 v1 x1 + y1 v2 x2 + y2 dx1 -1 l1 x1 x =2 v1l1 v2l2 1 x +y + v2 2 1 2 1 2 2 x2 + y2 dt x1 x2 =0= − dx1 v1l1 v2l2 l2 sin θ1 sin θ 2 = v1 v2 n1 sin θ1 = n2 sin θ 2 Physics 212 Lecture 25, Slide 10 10 Preflight 6 80 Snell’s Law: n1sinθ1 = n2sinθ2 60 40 20 n decreases ﬂ θ increases 0 Physics 212 Lecture 25, Slide 11 11 Total Internal Reflection θ1 > θc Simulation Total Internal Reflection Physics 212 Lecture 25, Slide 12 12 Preflight 8 70 60 50 40 θc clearly depends on both n2 and n1 30 20 10 0 Physics 212 Lecture 25, Slide 13 13 Intensity Anything looks like a mirror if light is just glancing off it. If two materials have the same n then its hard to tell them apart. Physics 212 Lecture 25, Slide 14 14 Preflight 4 70 60 50 40 30 20 10 0 Physics 212 Lecture 25, Slide 15 15 Polarization sin θ 2 = sin(90 − θ1 ) = cosθ1 n2 tan θ1 = Snell’s Law: n2 sin θ 2 = n2 cosθ1 = n1 sin θ1 n1 θ1 + θ 2 = 90 Physics 212 Lecture 25, Slide 16 16 A ball sits in the bottom of an otherwise empty tub at the ball front of the room. front Suppose N people sit high enough to see the ball (N = ). Physics 212 Lecture 25, Slide 17 17 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? BB A) More people will see the ball B) Same # will see the ball C) Less people will see the ball θA θw no wat ?? er water Snell’s Law: ray bent away from normal going from water to air Physics 212 Lecture 25, Slide 18 18 Preflight 10 BB 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. 70 60 50 40 30 DRAW SOME RAYS 20 10 0 Physics 212 Lecture 25, Slide 19 19 Example: Refraction at water/air interface • Diver’s illusion 97º Diver sees all of horizon refracted into a 97°cone θ1 = 90 n1 n1 1 sin θ 2 = sin 90 = = n2 n2 1.33 θ 2 = 48.5 Physics 212 Lecture 25, Slide 20 20 Exercise A meter stick lies at the bottom of a rectangular water tank of height 50cm. rectangular You look into the tank at an angle of 45o relative to vertical along a line that 45 relative skims the top edge of the tank. What is the smallest number on the ruler that you can see? ruler 45o 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. Physics 212 Lecture 25, Slide 21 21 45o Exercise A meter stick lies at the bottom of a rectangular water tank of height 50cm. rectangular You look into the tank at an angle of 45o relative to vertical along a line that 45 relative skims the top edge of the tank. What is the smallest number on the ruler that you can see? ruler 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 θR in the water ? A) θR = 28.3o B) θR = 32.1o C) θR = 38.7o BB Snell’s Law: nairsin(45) = nwatersin(θR) sin(θR) = nairsin(45)/nwater = 0.532 θR = sin-1(0.532) = 32.1o Physics 212 Lecture 25, Slide 22 22 45o Exercise A meter stick lies at the bottom of a rectangular water tank of height 50cm. rectangular You look into the tank at an angle of 45o relative to vertical along a line that 45 relative skims the top edge of the tank. What is the smallest number on the ruler that you can see? ruler nwater = 1.33 θR 50 cm 0 20 40 d 60 80 100 θR = 32.1o What number on the ruler does the laser beam hit ? A) 31.4 cm B) 37.6 cm C) 44.1 cm BB tan(θR) = d/50 d = tan(32.1) x 50cm = 31.4cm Physics 212 Lecture 25, Slide 23 23 45o Follow-Up Follow A meter stick lies at the bottom of a rectangular water tank of height 50cm. rectangular You look into the tank at an angle of 45o relative to vertical along a line that 45 relative 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) A) 25 cm B) 31.4 cm C) 32.0 cm D) 40.7 cm E) 44.2 cm BB Physics 212 Lecture 25, Slide 24 24 45o 45o nwater = 1.33 θR 50 cm 50 cm d = 50 cm d = 31.4 cm 0 20 40 60 80 100 0 20 40 60 80 100 θR = 32.1o 45o 50 cm nwater = 1.33 θR 0 20 d = 40.7 cm 40 25 cm + (31.4/2) cm 60 80 100 Physics 212 Lecture 25, Slide 25 25 More Practice A monochromatic ray enters a slab with n1 = 1.5 at an angle θb as shown θb n=1 TOP n1 = 1.5 BOTTOM θb n=1 BB (A) Total internal reflection at the top occurs for all angles θb, such that sinθb < 2/3 (B) Total internal reflection at the top occurs for all angles θb, such that sinθb > 2/3 (C) There is no angle θb (0 < θb < 90o) such that total internal reflection occurs at top. Snell’s law: n1 sin θ1 = n2 sin θ 2 nsinθ is “conserved” Ray exits to air with same angle as it entered !! Physics 212 Lecture 25, Slide 26 26 Follow-Up A ray of light moves through a medium with index of refraction n1 and is incident upon a second material (n2) at angle θ1 as shown. This ray is then totally reflected at the interface with a third material (n3). Which statement must be true? θ1 n1 n2 (A) n3 < n1 (B) n1 < n3 ≤ n2 (C) n3 ≥ n2 n3 θ1 If n1 = n3 n1 n2 n3 Want larger angle of refraction in n3 BB θ1 n3 < n1 Physics 212 Lecture 25, Slide 27 27 ...
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