Question

Unpolarized light passes through 2 ideal polaroid sheets. The axis of the first is vertical, and the axis of the second is at 30.0 degrees to the vertical. What fraction of the incident light is transmitted?

Answer 1

When plane polarized light of intensity $I_{max}$ arrives on single polarizing disc, its intensity changes depending on the angle between direction of polarization of light and the axis of polarizer $\theta$ . That intensity can be written as

$I = I_{max} cos^2\theta$

where, $I_{max}$ can be thought as initial intensity.

But, in this problem unpolarized light passes through a polaroid. Therefore, we can conclude that

its initial intensity is reduced by $\dfrac{1}{2}$ . Only then this light comes at second Polaroid .Then we can

calculate the fraction of transmitted light as

$\dfrac{I}{I_{max}} = \dfrac{1}{2}cos^230^\circ$

$\dfrac{I}{I_{max}} = \dfrac{3}{8} = 0.375$