3 pieces of Polaroid sheet (light intensity)

[togahockey15]

Homework Statement

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.

Homework Equations

I₀ = E²

(1/2)I₀ = I₁ (after 1^st sheet

then, I = E²cos²Θ

dsinΘ = mλ

The Attempt at a Solution

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

after that i don't know what to do...

 

[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.

 

[togahockey15]

thanks