1. Light Phenomena: Reflection, Refraction, Dispersion Updated 2014Jul23 Dr. Bill Pezzaglia Light & Optics

2. Outline A.The Law of Reflection 1.Reflection Law of Euclid and Heron 2.Images in a Mirror 3.Reflection Intensity B.The Law of Refraction 1.Fermat’s principle, Snell’s Law 2.Critical angle, total reflection 3.Refractive images C.Dispersion of Light 1.Prism disperses colors 2.Newton’s experiments 3.Sellmeier equation D.References 2

3. A. Reflection 1.The law of reflection (principle of least distance) 2.Image in a plane mirror 3.Intensity of Reflection 3

4. A. Law of Reflection 4

5. 1. The Law of Reflection (a) The Law of Reflection (Euclid 300 BC) 5

6. b. Principle of Least Distance Heron of Alexandria Light follows path of least distance (e.g. when reflecting off of water) 6 Which path should an ant take to get to the opposite end of the box fastest?

7. 2. Mirror and Virtual Images 7 “image” you “real” you mirror only needs to be half as high as you are tall. Your image will be twice as far from you as the mirror.

8. 3. Reflection & Transmission Speed of light can be calculated from electrical permittivity (  ) and magnetic permeability (  ) properties of the media Speed of light “v” in media is slower where “n” is index of refraction (about 1.5 for glass). As a wave (such as light) in media 1, with index n 1, enters a denser media (index n 2 ) where the speed changes, part of the wave will be reflected. Reflected intensity given by: For glass (n=1.5) we calculate that 4% is reflected, 96% transmitted 8

9. B. Refraction 1.Fermat’s Principle of Least Time & Snell’s law (1621) 2.Total Reflection (Snell’s window) 3.Refractive Images 9

10. 1. Fermat’s Principle Lifeguard Dilemma: What is the fastest path to drowning man? Note you can run twice as fast as you can swim. Run straight to river, then swim Run further to shore adjacent swimmer then swim Optimal path obeys Snell’s Law This is the path light (sound, any wave) will take! 10 Lifeguard Tower

11. 1b. Snell’s Law (1621) 11 Path of wave is bent toward normal when enters media with lower wavespeed (i.e. higher index of refraction)

12. 2a. Total Reflection (Snell’s Window) At the “critical angle” the refracted beam is at 90 , so it can’t get out. Greater than this “critical angle” there is 100% reflection Snell’s Window: from underwater a fish sees the entire area above surface in a cone. Outside the cone light is totally reflected 12

13. 2b. Total Reflection Total reflection will only occur if going from dense media to less dense! For glass (n=1.5) the critical angle is 42  Optical fibers are designed so the light is always 100% reflected, and bounces down the fiber. 13

14. 3. Refraction and Images The bottom of a river will appear to be shallower than it really is. Why? The apparent depth: 14

15. C. Dispersion 1.Phenomena 2.Newton’s Experiments 3.Sellmeier Equation 15

16. 1. Dispersion of a Prism Early theories were that a prism created color. White light goes in, colors come out. 12

17. 2a. The Components of Light 13 1672 Newton shows that the prism does not create color, it merely separates (“disperses”) the colors in the white light The second prism does not create more colors.

18. 2b. The Components of Light 14 1672 Newton further shows that a second prism can recombine colors to make white light. Hence white light is a mixture of all colors.

19. 3a. Speed in Media In media (such as glass) the speed is slower. This causes “refraction” the bending of light. The speed usually depends upon the wavelength, called “dispersion”. This causes the colors to be spread out. This work was done by Newton 23

20. 3b. Sellmeier Equation (1871) In media the speed of light depends upon wavelength (color) Sellmeier Equation (1871) shows index of refraction decreases for bigger wavelength, approaching n 0 Index of refraction goes to infinity at “color” 0 of media (e.g. green for emerald) 20

21. References http://www.thestargarden.co.uk/RefractionReflectionDiffraction.html http://www.olympusmicro.com/primer/lightandcolor/reflectionintro.html 21