1. Electromagnetic Waves Physics 202 Professor Vogel Lecture 13

2. Reflection and Refraction  Angles measured from normal !!  Angle of incidence (  1 )  Angle of reflection (  1 ’)  Angle of refraction (  2 )  Law of Reflection   1 ’ =  1  Law of Refraction n 2 sin  2 = n 1 sin  1

3. General Cases  n 2 > n 1  Light is bent towards the normal   2 <  1  e.g. air to glass  n 2 < n 1  Light is bent away from the normal   2 >  1  e.g. glass to air

4. Index of Refraction  Every material has an index of refraction that determines its optical properties  Indices of refraction determine bending, by law of refraction  Index of refraction also determines the speed of light within the material  v=c/n  generally, v<c

5. Consequences of Laws  Law of Reflection  The angle of reflection is equal to the angle of incidence (  1 ’ =  1 )  Light changes direction when it reflects  but our vision expects light to travel on a straight line  we see images where light appears to come from

6. Plane Mirror   1 ’ =  1  we see images where light appears to come from  Consider how light from your eye reflects from a mirror to get to your eye, so you can see it  repeat for light from your feet

7. Images in Plane Mirror  Upright  Same distance behind mirror as object is in front  Generally “front” is side light comes from.  Same size as object  Left and right are reversed.  Cardinal directions aren’t reversed.

8. Images in Plane Mirror Based on depth perception. Where do both the purple and the green rays appear to come from?

9. Images in 2-D corner Reflector  Can see an image in each mirror  Light can also reflect from both mirrors, then back to you.  You see image of image 1  Also see image of image 2  Both should be same place

10. Images in 2-D corner Reflector  Image of image  reflected twice  left and right exchanged twice  If you are right- handed, so is that image!

11. Images in Curved Mirrors  Concave mirror  think “cave”  like bowl of spoon  image is upright and larger – if object is close  image is inverted and smaller – if object is far  Convex mirror  like back of spoon  image is upright and smaller – any distance

12. Consequences of Laws  Law of Refraction n 2 sin  2 = n 1 sin  1  Light changes direction when it refracts  but our vision expects light to travel on a straight line  we see images where light appears to come from  Demo

13. Chromatic Dispersion  The index of refraction depends on the wavelength of light  In general, n is larger for shorter wavelengths  Blue light bent more than red  Incident white light is spread out into its constituent colors  Chromatic dispersion with raindrops causes rainbows

14. Chromatic Dispersion