Last question only currently using equation I_3= I_2 cos(theta)^2 theta being be

Question

Last question only currently using equation I_3= I_2 cos(theta)^2 theta being between 2nd and 3rd sheet and I've tried theta both at 22 and 44 degrees... please help, not sure what I'm doing wrong.

Two polarizing sheets have their transmission axes crossed so that no light gets through. A third sheet is inserted between the first two such that its transmission axis makes an angle 6 with that of the first sheet. Unpolarized light of intensity lo is incident on the first sheet. Find the intensity of the light transmitted through all three sheets for the following values of 6. (a) 45 through first sheet 1 0.5 through first two sheets 0.25 through all three sheets 0.125 (b) 6 22 through first sheet 0.5 through first two sheets 0.43 through all three sheets 0.37

Explanation / Answer

part (b)

for theta = 22

I1 = I0/2 = 0.5*I0

I2 = I1*(cos22)^2 = I0*(1/2)*(cos22)^2 = 0.43

I3 = I2*(cos(90-22))^2 = 0.43*(cos(90-22))^2*I0 = 0.06*I0

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