Lecture 23 1 Polarization of Electromagnetic Waves Polarization

Lecture 23 -1 Polarization of Electromagnetic Waves Polarization is a measure of the degree to which the electric field of an electromagnetic wave oscillates preferentially along a particular direction. Linear combination of many linearly polarized rays of random orientations partially polarized unpolarized linearly polarized Looking at E head-on components equal y- and zamplitudes unequal y- and zamplitudes

Lecture 23 -2 Polarizer: polarization by absorption An electric field component parallel to the transmission axis is passed by a polarizer; a component perpendicular to it is absorbed. transmission axis So if linearly polarized beam with E is incident on a polarizer as shown, Law of Malus Zero if = /2, I 0 if =0 If unpolarized beam is incident instead, Polarization can rotate in time if linearly polarized beams of different phases are combined.

Lecture 23 -3 Quiz Question 1 • A beam of un-polarized lights with intensity I is sent through two polarizers with transmission axis perpendicular to each other. What’s the outgoing light intensity? a) b) c) d) ½I 2 I 0 1. 5 I

Lecture 23 -4 Example: two polarizers This set of two linear polarizers produces LP (linearly polarized) light. What is the final intensity? – P 1 transmits 1/2 of the unpolarized light: I 1 = 1/2 I 0 – P 2 projects out the Efield component parallel to x’ axis: = 0 if = /2 (i. e. , crossed)

Lecture 23 -5 Intensity When unpolarized light is transmitted through a polarizer, the transmitted intensity is: I 1 = ½ I 0 When polarized light is transmitted through a polarizer, the transmitted intensity is: I 2 = I 1 cos 2θ

Lecture 23 -6 Quiz Question 2 Unpolarized light of intensity I 0 is sent through 3 polarizers, each of the last two rotated 45 from the previous polarizer so that the last polarizer is perpendicular to the first. What is the intensity transmitted by this system? a) 0. 71 I 0 b) 0. 50 I 0 c) 0. 25 I 0 d) 0. 125 I 0 e) 0

Lecture 23 -7 Polarization by reflection • When initially unpolarized light reflects from a boundary, it is possible for the reflected beam to become polarized • The requirement is that the reflected beam and transmitted (refracted) beam be �one another • Since the incident angle and the reflected angle must be equal, it can be shown that the necessary angle for incidence is: tan θB = n 2/n 1 θB = Brewter’s angle

Lecture 23 -8 Polarization by reflection

Lecture 23 -9 Example: Sunglasses cut down glare transmission axis

Lecture 23 -10 Quiz Question 3 Unpolarized light of intensity I 0 is sent through 3 polarizers. The second one is rotated 90 from the first polarizer, but the last one is again aligned in the same direction as the first. What is the intensity transmitted by this system? a) 0. 71 I 0 b) 0. 50 I 0 c) 0. 25 I 0 d) 0. 125 I 0 e) 0

Lecture 23 -11 Reflection from Fermat’s Principle The path taken by light traveling from one point to another is such that the time of travel is a minimum.

Lecture 23 -12 Refraction from Fermat’s Principle Snell’s law

Lecture 23 -13 Quiz Question 4 A light ray makes an angle of 42º with the normal to a glass-water surface on the glass side of the surface. The angle q in the water is A. 42º B. 36º C. 63º D. 49º E. 27º