Course Updates. Reminders: 1) Assignment #12 due Monday. 2) Start Optics (Chapter 33) 3) Last HW (#13 posted) due Monday, May 3rd

Transcription

1 Course Updates Reminders: 1) Assignment #12 due Monday 2) Start Optics (Chapter 33) 3) Last HW (#13 posted) due Monday, May 3rd

2 θ i = θ r n = 1 sinθ1 n2 sin θ 2 2

3 Index of Refraction Speed of light, c, in vacuum is 3x10 8 m/s Speed of light, v, in different medium can e v < c. index of refraction, n = c/v. frequency, f, does not change in wave eqn. of v = f λ, wavelength, λ, depends on medium, λ = v/f = c/nf = λ 0 /n In some media, n, depends on f, this is called dispersion. 3

4 Waves, wave front, rays (Y&F section 33.2) Plane waves moving in +x direction r E r B ( x, y, z, t) = E0 yˆ cos( kx ωt) ( x, y, z, t) = B zˆ cos( kx ωt) 0 Wave front is a surface of constant phase E field Wave front (y-z plane surface of constant phase) y Ray propagation z x 4

5 Huygen s Principle (Y&F section 33.7) Huygen s principle; a wave front can e a source of secondary wavelets the spread out in all directions at the speed of propagation in the medium. The envelope of leading edges forms a wave front. This principle was stated y Huygen in 1678, it is derivale from Maxwell s eqn. It is a geometrical description of ray propagation. vt Plane wave example; Secondary wavelets create another wave front (plane) 5

6 Reflection from Huygen s Principle Consider wave fronts, separated y vt, the incident wave fronts in contact with the surface will create a wavelets according to Huygen s Principle and leads to another reflected wave front. The result is θ i = θ r reflected wave front Incident wave front vt vt vt ray diagram vt θ r θ i θ i θ r θ i = θ r Reflection Law 6

7 Refraction from Huygen s Principle Now the speed changes, from medium a to medium, so the Speed may change and the wavefront spacing differs. L sinθ a = v a t = ct/n a L sinθ = v t= ct/n Medium a, v a =c/n a Medium, v =c/n θ L v t v t Wave front L v a t θ a v a t Wave front = n sinθ n a sinθ a Snell s Law 7

8 Snell s Law (law of refraction) Incident ray θ a normal Wave front Medium a, v a =c/n a Medium, v =c/n θ Refracted Wave front Refracted ray θ θ a Angles are usually given relative to normal to plane = n sinθ n a sinθ a Snell s Law 8

9 Question 1 A ray of light passes from into water with an angle of incidence of 30 o. Which of the following quantities does not change as the light enters the water. a) Wavelength ) frequency c) speed of propagation d) direction of propagation. 9

10 Question 1 A ray of light passes from into water with an angle of incidence of 30 o. Which of the following quantities does not change as the light enters the water. a) Wavelength ) frequency c) speed of propagation d) direction of propagation. 10

11 Question 2 Which of the following ray diagrams could represent the passage of light from through glass and ack to? (n =1 and n glass =1.5) (a) () (c) glass glass glass 11

12 Question 2 Which of the following ray diagrams could represent the passage of light from through glass and ack to? (n =1 and n glass =1.5) (a) () (c) glass θ 1 θ 2 glass glass The ehavior of these rays is determined from Snell s Law: n = 1 sinθ1 n2 sin Since n(glass) > n(), sinθ (glass) < sinθ (). Therefore, moving from to glass, ray will end toward normal. this eliminates (a). Moving from glass to, ray will end away from normal. this eliminates (c). As a matter of fact, the final angle in must e equal to the initial angle in!! 12 θ 2

13 EXAMPLE, from into glass; θ a Suppose we have light in (n=1) incidence on glass (n=1.55) at an angle θ a =45 deg. What is the angle of the refracted light, θ? θ n sinθ = n (1)sin ( 45 ) = (1)sin sinθ = 1.55 θ = 27 a glass (1.55)sinθ ( 45 ) sinθ =

14 EXAMPLE, from glass into ; Suppose we have light in glass (n=1.55) incident into at an angle θ a =30 deg. What is the angle of the refracted light, θ? n glass sinθ = n (1.55)sin sinθ θ = = 51 a ( 30 ) = (1.55)sin sinθ (1)sinθ ( 45 ) = θ a θ 14

15 The ANITA Concept Typical alloon field of regard ~4km deep ice! 15

16 Refraction limits ANITA! E S U ANITA at float (123Kft) Seen through amateur telescope from the South Pole Size of the Rose Bowl! (thanks to James Roth) 16

17 Mini-Antarctica at Stanford Linear Accelerator 17

18 SLAC T486 θ θ a 2 mile long accelerator 28 Billion electron Volts If you ve driven I-280 etween San Francisco and San Jose 18

19 Prolem!!! θ θ a ice There is no escape!!! n ice sinθ = n (1.8) sin sinθ θ = = 90 a ( 34 ) = (1.8) sin sinθ (1) sinθ ( 34 ) =

20 Prolem θ a θ Solution = cut! ~7degrees ice θ =?? n ice sinθ = n (1.8) sin ( 34 ) sinθ = (1.8) sin a θ = 90 sinθ = (1) sinθ ( 34 ) = 1.0 n ice sinθ = n (1.8) sin sinθ a ( 27 ) = (1.8) sin θ = 54.8 sinθ = (1) sinθ ( 27 ) θ = 0.82 θ a ice θa θ ice 20

21 Mini-Antarctica at Stanford Linear Accelerator 21 Cut ~7degrees! (jackhammers, chainsaws, mauls not shown)

22 10 tons ice 22

23 23

24 Let there e light! (OK, radio) 24

25 Suppose you are stranded on an island with no food. You see a fish in the water. Where should you aim your spear to hit the fish? ANSWER; do not aim directly at the apparent position of the fish. Aim at the inside of the fish. 25

26 Suppose in the previous question instead of a spear you had a high power laser to simultaneously kill and cook the fish (in the water). Where should you aim the laser?? ANSWER; aim directly at apparent fish position as the laser eam will refract to the correct fish position. 26

27 For next time Homework #12 posted due Monday The home stretch: optics/optical phenomenon 27

28 Key Instrument pieces CSBF CIP Battery ox Instrument ox 28

29 Launch: Decemer 15, 2007 (after almost 2 agonizing weeks of waiting) Courtesy Kim Palladino A flawless launch CSBF truly professional After day after day after day of false starts, we were really ready to go 29