A polarizer with its transmission axis oriented at an angle q with respect to the z-axis is placed in the path of a linearly polarized beam of light propagating along the x-axis.  The beam is polarized at an angle a with respect to the z-axis.

(a) If the two field components of the light beam have amplitude factors A_y and A_z, then in terms of the ratio A_y/A_z, what fraction of the intensity is transmitted through the polarizer when it is oriented at angle q = 90° (parallel to the y axis)?  What fraction is transmitted when it is oriented at angle q = 0° (parallel to the z axis)? 

(b) Calculate the fraction transmitted for both q = 0° and q = 90° for the following orientations of the linear polarization: a = 0°, 45°, and 60°.

Problem 2:

Show that a birefringent plate with a thickness of L = l/(2Dn) produces linearly polarized light with an angle of a = –45° when linearly polarized light with an angle of a = +45° is incident on the plate.  If the birefringence is Dn = 10^–5, how thick should such a plate be for a HeNe laser (l = 633 nm)?

Problem 3:

Suppose you want to shine a linearly polarized laser beam through a glass window (n = 1.5) with no loss (no reflection).
If the incident beam is in air, what should the angle of incidence be to achieve Brewster’s Angle
What is the angle of the refracted rays inside the glass?  Does this angle satisfy Brewster’s condition at the second (glass-to-air) interface of the window?

Problem 4:

Ignoring interference (i.e., considering only the spatially averaged intensity), what fraction of s-polarized light is transmitted through the window in problem 3 if the incident beam is at Brewster’s Angle?  To find this fraction, calculate the amount of s-polarized intensity reflected at each of the interfaces.  What is the ratio of the transmitted p-polarized portion of the beam to the s-polarized portion?

Problem 5:

Problem 6: