A clear sheet of polaroid is placed on the top of similar sheet so that their axes make an angle sin−1(35) with each other. The ratio of intensity of the emergent light to that of unpolarised incident light is k25. Find k.

Solution:

If I is the intensity of the incident unpolarised light, the intensity transmitted by the first is I/2. This is the intensity of incident light on the second polaroid. Intensity transmitted by the second polaroid is $\frac{I}{2} \cos^{2} θ,$ where is $θ$ the angle between the axes.

Here, $sinθ = \frac{3}{5}$ therefore, $cosθ = \frac{4}{5},$

$I' = \frac{I}{2} \cos^{2} θ = \frac{I}{2} {(\frac{4}{5})}^{2} = \frac{8}{25} I$