1. PHY2054 Fall 2011 The second exam is on Tuesday Nov. 8, 8:20-10:10PM. Please check the room assignments on the exam page. HW set 7 was due Monday 10/24. HW set 8 due on Monday 10/31 Kumar’s Tea and Cookies on Tuesday 10/25 at 5 PM in NPB 2175. Questions? Ask…

2. Chapter 22 Reflection and Refraction of Light

3. Last time Light is an electromagnetic wave. c = 1/ √(ε o μ o ) = fλ B = E/c I = E max B max /2μ o p = U/c C = 2.99792 x 10 8 m/s = 0.9836 ft/ns Doppler effect f o = f s (1 ±u/c)

4. Reflection and Refraction Laws of reflection Laws of refraction Total internal reflection The rainbow

5. 5 The Sun is about 1.5 × 10 11 m away. The time for light to travel this distance is about: A. 4.5 × 10 18 s B. 8 s C. 8 min D. 8 hr E. 8 yr

6. Geometric Optics – Using a Ray Approximation Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media The ray approximation is used to represent beams of light A ray of light is an imaginary line drawn along the direction of travel of the light beams

7. Ray Approximation A wave front is a surface passing through points of a wave that have the same phase and amplitude The rays, corresponding to the direction of the wave motion, are perpendicular to the wave fronts

8. Reflection of Light A ray of light, the incident ray, travels in a medium When it encounters a boundary with a second medium, part of the incident ray is reflected back into the first medium This means it is directed backward into the first medium

9. Specular Reflection Specular reflection is reflection from a smooth surface The reflected rays are parallel to each other All reflection in this text is assumed to be specular

10. Diffuse Reflection Diffuse reflection is reflection from a rough surface The reflected rays travel in a variety of directions Diffuse reflection makes the dry road easy to see at night

11. Law of Reflection The normal is a line perpendicular to the surface It is at the point where the incident ray strikes the surface The incident ray makes an angle of θ 1 with the normal The reflected ray makes an angle of θ 1 ’ with the normal

12. Law of Reflection, cont The angle of reflection is equal to the angle of incidence θ 1 = θ 1 ’ The reflected ray, the incident ray and the normal are all coplanar.

13. θ+β = 120°

14. Refraction of Light When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray is reflected and part of the ray enters the second medium The ray that enters the second medium is bent at the boundary This bending of the ray is called refraction

15. Refraction of Light, cont The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane The angle of refraction, θ 2, depends on the properties of the medium (Snell’s law) n 1 sin θ 1 = n 2 sin θ 2

16. Following the Reflected and Refracted Rays Ray  is the incident ray Ray  is the reflected ray Ray is refracted into the lucite Ray  is internally reflected in the lucite Ray is refracted as it enters the air from the lucite

17. Refraction Details, 1 Light may refract into a material where its speed is lower The angle of refraction is less than the angle of incidence The ray bends toward the normal

18. Refraction Details, 2 Light may refract into a material where its speed is higher The angle of refraction is greater than the angle of incidence The ray bends away from the normal

19. The Index of Refraction When light passes from one medium to another, it is refracted because the speed of light is different in the two media The index of refraction, n, of a medium can be defined

20. Index of Refraction, cont Some values of n For a vacuum, n = 1 For other media, n > 1 n is a unitless ratio As the value of n increases, the speed of the wave decreases

21. Frequency Between Media As light travels from one medium to another, its frequency does not change Both the wave speed and the wavelength do change The wavefronts do not pile up, nor are created or destroyed at the boundary, so ƒ must stay the same

22. Index of Refraction Extended The frequency stays the same as the wave travels from one medium to the other v = ƒ λ The ratio of the indices of refraction of the two media can be expressed as various ratios

24. Some Indices of Refraction