Lect25 - Physics 212 Lecture 25 Physics 212 Lecture 25,...

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Unformatted text preview: Physics 212 Lecture 25 Physics 212 Lecture 25, Slide 1 Physics Music Who is the Artist? A) B) C) D) E) Carmen McRae Billie Holiday Sarah Vaughan Dinah Washington Ella Fitzgerald Why? I heard her on the radio yesterday for the heard first time in a long time first Totally classic and unique voice Physics 212 Lecture 25, Slide 2 Physics Your Comments “Finally we're in optics! YAY!!!!!” “Everything. Could you also explain the Everything. question about the pool?” question We will defnitely discuss the We pool.. a small demo, even pool.. “Can you explain Brewster's Angle again? Can Im not sure what the double angles and circles actually represent.” circles Will Do.. “problem solving for these problems” We will do some refraction We problems today problems 40 “How come 3 of my comments were How posted last semester in physics 211 and none were posted this semester??? Hopefully this makes it. :)” Hopefully 30 20 10 0 05 Confused Confident Physics 212 Lecture 25, Slide 3 Physics Let’s start with a summary: from n2 to n1 Physics 212 Lecture 25, Slide 4 Physics 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 Physics Preflight 2 BB A B C What about the wave must be the same on either side ??? 50 Observers in both media must agree on the frequency of vibration of the molecules 40 30 20 10 0 Physics 212 Lecture 25, Slide 6 Physics Reflection Physics 212 Lecture 25, Slide 7 Physics Refraction: Snell’s Law D sin θ 2 D sin θ1 = c / n2 c / n1 n2 sin θ 2 = n1 sin θ1 Physics 212 Lecture 25, Slide 8 Physics 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 Physics A x1 l1 Same Principle works for Light !! y1 D y2 l2 B x2 Time from A to B : To find minimum time, differentiate t wrt x1 and set = 0 How is x2 related to x1? Setting dt/dx1 = 0 l l t= 1+ 2 = v1 v2 2 2 2 2 x1 + y1 x2 + y 2 + v1 v2 dt x1 x2 dx2 = + 2 2 2 2 dx1 v1 x1 + y1 v2 x2 + y2 dx1 x2 = D − x1 x1 x − 2 =0 v1l1 v2l2 dx2 = −1 dx1 sin θ1 sin θ 2 = v1 v2 v = c/n n1 sin θ1 = n2 sin θ 2 Physics 212 Lecture 25, Slide 10 Physics Preflight 6 70 Snell’s Law: n1sinθ1 = n2sinθ2 60 50 40 30 20 n decreases fl θ increases 10 0 Physics 212 Lecture 25, Slide 11 Physics Total Internal Reflection NOTE: n1 > n2 implies θ2 > θ1 θ1 > θc BUT: θ2 has max value = 90o !! Total Internal Reflection Physics 212 Lecture 25, Slide 12 Physics Preflight 8 70 60 50 40 θc clearly depends on both n2 and n1 30 20 10 0 Physics 212 Lecture 25, Slide 13 Physics 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 Physics Polarization θ1 + θ 2 = 90o sin θ 2 = sin( 90o − θ1 ) = cos θ1 Snell’s Law: n2 sin θ 2 = n2 cosθ1 = n1 sin θ1 n2 tanθ1 = n1 Physics 212 Lecture 25, Slide 15 Physics Preflight 4 BB 70 o = horizontal 60 50 40 30 20 10 0 Physics 212 Lecture 25, Slide 16 Physics 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 Physics 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 Physics 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 Physics Example: Refraction at water/air interface • Diver’s illusion 97º Diver sees all of horizon refracted into a 97°cone θ1 = 90 o n1 n1 1 o sin θ 2 = sin 90 = = n2 n2 1.33 θ 2 = 48.5o Physics 212 Lecture 25, Slide 20 Physics Exercise 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. and Physics 212 Lecture 25, Slide 21 Physics 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 Physics 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 Physics 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 Physics 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 Physics 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 Physics 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 Physics ...
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This note was uploaded on 02/09/2012 for the course PHYSICS 212 taught by Professor Mestre during the Spring '11 term at University of Illinois at Urbana–Champaign.

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