# Homework Help: 3 pieces of Polaroid sheet (light intensity)

1. Apr 7, 2009

### togahockey15

1. The problem statement, all variables and given/known data
Unpolarized light of intensity I0 passes through two pieces of Polaroid sheet. The second piece is rotated so that the intensity of the transmitted light goes to zero. A
third piece of Polaroid is inserted between the two pieces. Calculate the intensity as
a function of the angle Θ that the axis of the middle piece makes with the axis of the
ﬁrst piece. By calculating the derivative of the intensity as a function of angle, ﬁnd
the angle that maximizes the intensity for this three-sheet arrangement.

2. Relevant equations

I0 = E2

(1/2)I0 = I1 (after 1st sheet

then, I = E2cos2Θ

dsinΘ = mλ

3. The attempt at a solution

After passing the first sheet, I = (1/2) I0
Then, (1/2)I0 = E2cos2Θ

after that i dont know what to do...

2. Apr 8, 2009

### rl.bhat

Two Polaroid are in crossed position. When the third Polaroid is rotated through an angle theta Intensity through it is I = E^2cos^2(theta).Axis of the second Polaroid makes an angle (90 - theta) with the axis of the middle sheet. Hence intensity of the light from the second sheet I' = E^2cos^2(theta)*cos^2(90 - theta)
or I' = E^2cos^2(theta)*sin^2( theta)
Further simplify it. Differentiate with respect to theta and equate it to zero to get the angle for maximum and minimum intensity.

3. Apr 8, 2009

thanks