3) Initially Ann lured light is sent into a system of three polanzing sheets. Th

Question

3) Initially Ann lured light is sent into a system of three polanzing sheets. The angles and 6 of the polarizing directions are measured counterclockwise from the positive direction of the x-axis (they are not drawn to scale). Angles &, and 6 are fixed, but angle 6, can be varied. The figure below gives the intensity of the light emerging from sheet 3 as a function of G (The scale of the intensity axis is not indicated.) (a) What percentage of the light's initial intensity is transmitted by the 3 sheet system when 6-90 0 0° 60° 120 180° e, (b) From the graph, the peak intensity occurs when polarizer #2 is at about 15°. In a few words, describe the process you could use to more precisely find the exact angle for polarizer #2 which results in maximum final intensity. Hint: Think Calculus.

Explanation / Answer

a] intensity coming out of sheet 3 is given by:

i = i0/2 * cos [ theta2 - theta1] * cos [theta3 - theta2]

i/i0 = 0.5 *(cos [ 90 degree - theta1])^2 * (cos [theta3 - 90 degree])^2

= 0.5 *( sin theta1)^2 (sin theta3)^2

percentage = 100*0.5 *( sin theta1)^2 (sin theta3)^2

= 50*( sin theta1)^2 (sin theta3)^2 %

b] We will find the maxima of the graph.

It can be found by equating the derivative to zero

di /dtheta = 0

then finding the smallest solution of the derivative equation above.

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