1. Electromagnetic Waves Physics 202 Professor Vogel (Professor Carkner’s notes, ed) Lecture 12

2. Incident Polarized Light  For polarized light incident on a sheet of Polaroid, the resultant intensity depends on the angle  between the original direction of polarization and the sheet  The new electric field becomes: E = E 0 cos   Since I depends on E 2 it becomes: I = I 0 cos 2   This is only true for polarized light  For unpolarized light that pass through two polarizing sheets,  is the angle between the two sheets

3. Multiple Sheets

4. Sheet Angles

5. Polarization By Reflection  Light reflected off of a surface is generally polarized  This is why polarized sunglasses reduce glare  When unpolarized light hits a horizontal surface the reflected light is partially polarized in the horizontal direction and the refracted light is partially polarized in the vertical direction

6. Reflection and Refraction  When light passes from one medium to another (e.g. from air to water) it will generally experience both reflection and refraction  Reflection is the portion of the light that does not penetrate the second medium but bounces off of the surface  Refraction is the bending of the portion of the light that does penetrate the surface

7. Geometry  The normal line is a line perpendicular to the interface between the two mediums  Angles  Angle of incidence (  1 ): the angle between the incident ray and the normal  Angle of reflection (  1 ’): the angle of the reflected ray and the normal  Angle of refraction (  2 ): the angle of the refracted ray and the normal

8. Laws  Law of Reflection  The angle of reflection is equal to the angle of incidence (  1 ’ =  1 )  Law of Refraction  The angle of refraction is related to the angle of incidence by: n 2 sin  2 = n 1 sin  1  Where n 1 and n 2 are the indices of refraction of the mediums involved

9. Index of Refraction  Every material has an index of refraction that determines its optical properties  n = 1 for vacuum  We will approximate air as n = 1 also  n is always greater than or equal to 1  Large n means more bending

10. General Cases  n 2 = n 1  No bending   2 =  1  e.g. air to air  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

11. Total Internal Reflection  Consider the case where  2 = 90 degrees  In this case the refracted light is bent parallel to the interface  For angles greater than 90 there is no refraction and the light is completely reflected   2 > 90 when the incident angle is greater than the critical angle  c n 1 sin  c = n 2 sin 90  c = sin -1 (n 2 /n 1 )  This is the case of total internal reflection, where no light escapes the first medium

12. 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

13. Chromatic Dispersion

14. Brewster Angle  At a certain angle, known as the Brewster angle, the reflected light is totally polarized  At  B the reflected and refracted rays are perpendicular to each other, so  B +  r = 90  Since n 1 sin  B = n 2 sin  r we get  B = tan -1 (n 2 /n 1 )  If we start out in air n 1 = 1 so:  B = tan -1 n  This is Brewster’s Law