Optics Polarization Birefringence

Transcription

1 Optics Polarization Birefringence Lana Sheridan De Anza College June 21, 2018

2 Last time the interferometer and gravitational waves polarization Brewster angle

3 Overview polarization birefringence Rayleigh scattering

4 the reflecting surface and perpendicular to those the reflected ray (perpendicular to the dots and parallel to the blue arrow) send no energy in this direction. perpendicular to the page. represented by the dots. Creating Polarized Light: by Reflection Incident u 1 u 1 Reflected Incident u p u p Reflected n 1 n 2 90 n 1 n 2 u 2 u 2 a Refracted We can obtain an expression relating the polarizing angle to the index of refraction of the reflecting substance by using Figure 38.28b. From this figure, we see that When u p 1 90 the 1 ureflected ; therefore, and refracted u rays 2 uare p. Using perpendicular, Snell s law of the refraction (Eq. 35.8) gives n 2 n 1 5 sin u 1 sin u 2 5 sin u p sin u 2 b Refracted The dipoles in the surface cannot create a ray that has an E-field oscillating in the direction that the ray travels. reflected ray is completely polarized parallel to the surface.

5 y m es field oscillations parallel to the reflecting surface and perpendicular to those Creating Polarized Light: by Reflection perpendicular to the page. electric field oscillations represented by the dots. oscillating in the direction of the reflected ray (perpendicular to the dots and parallel to the blue arrow) send no energy in The value of the incident angle for the reflected and transmitted this direction. rays to be perpendicular, θ p is called Brewster s angle. - Incident u 1 u 1 Reflected Incident u p u p Reflected n 1 n 2 90 n 1 n 2 u 2 u 2 a Refracted Notice, θ 2 = 90 θ p. From Snell s Law: We can obtain an expression relating the polarizing angle to the index of refraction of the reflecting substance by using Figure 38.28b. From this figure, we see that u p u ; n 1 therefore, sin θ p u= n 2 cos(θ 2 u p. Using p ) Snell s law of refraction (Eq. 35.8) gives So, n 1 sin θ p = n 2 sin(90 θ p ) n 2 5 sin u 1 5 sin ( u p nθ 1 p = sin tan u 1 n2 2 sin u n 2 1 Because sin u 5 sin (90 2 u ) 5 cos u, we can write this expression as n /n 5 b ) Refracted

6 ary ray and n E ordinary (O) ray and an extraordi- Creating Polarized Light: Birefringent Materials nary (E) ray (not to scale). ordinary Calcite and quartz are examples of crystals that have a special t material property: at an the speed of light (phase velocity) is not the same in all directions. The E and O rays propagate ll cause the two The speed of a ray with depends the same on both velocity the along the direction it travels and Figure the optic axis. the direction of polarization. ll directions. If Optic axis E 38.30, the ordiof refraction n E extraordinary rence in speed optic axis. For S O ries from for n O and the n Table rough the crysn Figure Figure A point source S S is a point source emitting in all directions: the wavefronts don t one formed by inside a double-refracting crystal remain spherical for produces one type a spherical of polarization wave front (E-ray).

7 38.6 Polarization of Light Waves 1179 Creating Polarized Light: Birefringent Materials There are two refracted rays in a birefringent material: hich the atoms ture of Figure atoms are disan amorphous ctions. That is, such as calcite. In these maten the plane of dices of refracgent materials. split into an mutually permaterial. The ary ray and n These two rays are polarized in mutually perpendicular directions. Unpolarized light Calcite E ray O ray Figure Unpolarized light The ordinary ray (O) incident and at thean extraordinary angle to the optic ray (E). Both have different polarizations. axis in a calcite crystal splits into an ordinary (O) ray and an extraordi-

8 no light in this direction. Creating Polarized Light: Scattering Unpolarized light Air molecule Vari follows. d, wher tion d, in the a let light when su (violet) Whe the sca sensitiv with les to viole toward

9 Scattering depends on Wavelength When light is scattered by particles much smaller than the wavelength of the radiation (Rayleigh scattering), the intensity of the scattered light goes as: I = I 0 (const.) λ 4 (1 + cos 2 θ) (θ is the scattering angle.) Shorter wavelengths (violet) are scattered more intensely.

10 Why the Sky is Blue: Rayleigh Scattering The amount (intensity) of the light scattered by small particles depends on the wavelength: I 1 λ 4 shorter wavelength light is scattered more opalescent glass 1 Left, Robert A. Rohde, Wikipedia; right, user optick,

11 This Course Questions we wanted to answer: How does an airplane wing create an upward lifting force? Why does hot metal start to glow read when heated? When a block of ice is left out at room temperature and pressure it will melt. Why does this happen? Why is it not uncommon to see a glass cup fall and shatter, but we never see a pile of broken glass reassemble itself into a cup? Why can you hear someone s voice when they are still around a corner from you, but you can t see them? Why is the sky bright during the day? Why is the daytime sky blue?

12 Summary polarization birefringence scattering Final Exam 9:15-11:15am, Tuesday, June 26. Homework Serway & Jewett: prev: Ch 38, onward from page OQs: 1, 7; Probs: 45, 49, 51, 63, 65, 70 new: Ch 38, onward from page Prob: 75