Wavefronts and Rays. When light or other electromagnetic waves interact with systems much larger than the wavelength, it s a good approximation to

Transcription

1 Chapter 33: Optics

2 Wavefronts and Rays When light or other electromagnetic waves interact with systems much larger than the wavelength, it s a good approximation to Neglect the wave nature of light. Consider that the light travels in straight lines, called rays, while in a uniform medium. Rays are perpendicular to the wavefronts and the rays direction is that of the wave propagation. The ray approximation is also known as geometrical optics.

3 Reflection When light reflects from a surface, the incident and reflected rays make the same angle with the normal to the surface. For smooth surfaces, parallel rays all reflect at the same angle. The angles are equal (locally) even for rough surfaces. But because of the roughness, the light comes off in random directions. This is called diffuse reflection.

4 The Plane Mirror

5 Question You would like to buy a full-length mirror which allows you to see yourself from head to toe. The minimum height of the mirror is A) half your height. B) two-thirds of your height. C) equal to your height. D) depends on distance you stand from mirror

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7 Refraction Refraction is the bending of light as it crosses the interface between two different transparent media. Refraction occurs because the wave speed differs in different media. For light, the index of refraction n describes the speed change. The speed of a wave in a medium is v = c/n. The angles of incidence and refraction are related by Snell s law: n 1 sin 1 = n 2 sin 2

8 Derivation of Snell s Law 1 x =sin 1 2 x =sin 2 1 sin 1 = i = 2 sin 2 tc/n i tc n 1 sin 1 = tc n 2 sin 2 n 1 sin 1 = n 2 sin 2

9 Clicker question The figure shows the path of a light ray through three different media. Rank the media in order of their refractive indices. A. B. C. D. n1 > n2 > n3 n3 > n1 > n2 n > n > n n > n > n 2 1 3

10 Example: Sunlight strikes the surface of a lake. A diver sees the Sun at an angle of 42.0 with respect to the vertical. What angle do the Sun s rays in air make with the vertical? incident wave n 1 = 1.00; air n 2 = 1.33; water θ 1 surface 42 Transmitted wave Normal

11 Example: Sunlight strikes the surface of a lake. A diver sees the Sun at an angle of 42.0 with respect to the vertical. What angle do the Sun s rays in air make with the vertical? incident wave n 1 = 1.00; air n 2 = 1.33; water Transmitted wave 42 θ 1 Normal n 1 surface sinθ 1 = sinθ ( 1.00) sinθ = ( 1.333) 1 sinθ1 = θ = n 2 2 sin 42

12 Question 23.8 Gone Fishin I To shoot a fish with a gun, should you aim directly at the image, slightly above, or slightly below? 1) aim directly at the image 2) aim slightly above 3) aim slightly below

13 From: Sight

14 Mirages

15 Total internal reflection The angle of incidence for when the angle of refraction is 90 is called the critical angle. n n 1 1 sinθ = sinθ sinθ 1 c c = = n n 2 2 n n 2 1 sinθ 2 sin90 = n 2 If the incidence angle is greater than the critical angle, the beam can not refract but is completely reflected

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18 Fiber Optics

19 Dispersion Index of refraction depends on wavelength If a beam of white light is incident on silicate glass (say with θ inc =45 ) which color bends more (due to refraction)? 1. blue 2. yellow 3. red 4. all refract the same

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22 Polarization dav_optics/examples/polarization.html

23 Polarizers Poloroid filter: Electric field does work on electrons along strands of filter, causing E field in that direction to be attenuated For unpolarized light: I transmitted = I incident <cos 2 >= 1 2 I incident

24 Clicker Question An unpolarized beam of light passes through 2 Polaroid filters oriented at 45 o with respect to each other. The intensity of the original beam is I o. What is the intensity of the light coming through both filters? I o A: (1/1.4)I o B: (1/2)I o C: (1/4)I o D: (1/8)I o E: None of the above c

25 QuickCheck 34.9 Unpolarized light, traveling in the direction shown, is incident on polarizer 1. Does any light emerge from polarizer 3? A. Yes. B. No.

26 Example of Polarized Light: Scattering of sunlight:

27 Example of Polarized Light: Reflected light from medium with higher index of refraction: Reflected light is more polarized with electric field parallel to the surface