Lecture 24: TUE 20 APR 2010 Ch : E&M Waves

Transcription

1 Physics 2102 Jonathan Dowling Lecture 24: TUE 20 APR 2010 Ch : E&M Waves

2 Radiation Pressure Waves not only carry energy but also momentum. The effect is very small (we don t ordinarily feel pressure from light). If light is completely absorbed during an interval Dt, the momentum transferred is given by! u and twice as much if reflected. Newton s law: F =! p =! p! t Now, supposing one has a wave that hits a surface of area A (perpendicularly), the amount of energy transferred to that surface in time Dt will be! U = IA! t therefore Radiation pressure: c! p = IA! t c p r = I c (total absorption), p r = 2I c I (total reflection) F = IA c A F [Pa=N/m 2 ]

3 Radiation Pressure & Comet Tails

4 Solar Sails: Photons Propel Spacecraft! StarTrek DS9 NASA Concept NASA Demo

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6 Radio transmitter: EM waves: polarization If the dipole antenna is vertical, so will be the electric fields. The magnetic field will be horizontal. The radio wave generated is said to be polarized. In general light sources produce unpolarized waves emitted by atomic motions in random directions.

7 EM Waves: Polarization Completely unpolarized light will have equal components in horizontal and vertical directions. Therefore running the light through a polarizer will cut the intensity in half: I=I 0 /2 When polarized light hits a polarizing sheet, only the component of the field aligned with the sheet will get through. E y = E cos(! ) And therefore: I = I 2 0 cos!

8 Example Initially unpolarized light of intensity I 0 is sent into a system of three polarizers as shown. What fraction of the initial intensity emerges from the system? What is the polarization of the exiting light? Through the first polarizer: unpolarized to polarized, so I 1 =½I 0. Into the second polarizer, the light is now vertically polarized. Then, I 2 = I 1 cos 2 60 o = 1/4 I 1 = 1/8 I 0. Now the light is again polarized, but at 60o. The last polarizer is horizontal, so I 3 = I 2 cos 2 30 o = 3/4 I 2 =3 /32 I 0 = I 0. The exiting light is horizontally polarized, and has 9% of the original amplitude.

9 Reflection and Refraction When light finds a surface separating two media (air and water, for example), a beam gets reflected (bounces) and another gets refracted (bends). Law of reflection (Light Bounces): the angle of incidence θ 1 equals the angle of reflection θ 1. θ 1 = θ 1 Law of Refraction (Light Bends):!! n 2 sin! 2 = n 1 sin! 1!! Snell's Law n is the index of refraction of the medium. In vacuum, n = 1. In air, n ~ 1. In all other media, n > 1.

10 Plastic Glass Speed of Light is Slowed n>1 n=1 n>1 Hits Sand Turns Left Road v L v! c / n!!!!&!!!!n " 1!!!!!#!!!!v $ c v R

11 Example Water has n=1.33. How much does a beam incident at 45 o refracts? n 2 sin θ 2 = n 1 sin θ 1 sin θ 2 = (n 1 /n 2 ) sin θ 1 =(1/1.33) sin 45 o = θ 2 = 32 o

12 Water on Desert Road Illusion The index of refraction decreases with temperature: the light gets refracted and ends up bending upwards. We seem to see water on the road, but in fact we are looking at the sky!

13 Water on the Desert Road Mirage

14 Chromatic Dispersion The index of refraction depends on the wavelength (color) of the light.

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16 The Single Rainbow

17 The Double Rainbow Total Internal Reflection!

18 Total Internal Reflection From glass to air, the law of refraction uses n 2 <n 1, so θ 2 > θ 1 : it may reach 90 o or more: the ray is reflected instead of refracted. θ 2 n 2 ~1 Condition for TIR: n 2 sinθ 2 = n 1 sinθ 1 & θ 2 90 θ 1 n 1 >1 For glass (fused quartz) n=1.46, and the critical angle is 43 o : optical fibers!

19 Fish Underwater Can t See Entire Sky! Total Internal Reflection Zone

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21 The cut of the diamond favors total internal reflection. Most rays entering the top of the diamond will internally reflect until they reach the top face of the diamond where they exit. This gives diamonds their bright sparkle. A fiber optic is a glass "hair" which is so thin that once light enters one end, it can never strike the inside walls at less than the critical angle. The light undergoes total internal reflection each time it strikes the wall. Fiber optic cables are used to carry telephone and computer communications.

22 Fiber Optic Cables

23 Underwater Telephone and Internet Fiber Telecom Cables

24 FIBER OPTIC GUIDED MISSILE

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26 Polarization By Reflection Different polarization of light get reflected and refracted with different amplitudes ( birefringence ). At one particular angle, the parallel polarization is NOT reflected at all! This is the Brewster angle θ B, and θ B + θ r = 90 o. n o 1 sin! n2 sin(90 "#!) = n2 # = cos#! Polarizing Sunglasses tan "! = n n 2 1

27 Polarized Sunglasses