Wave OpticsMedium
Question
The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at ${22.5}^{\circ}$ from the polarization axis of one of the polaroids, is ( $//s_{s}$ is the intensity of polarised light after passing through the first polaroid):
Options
A.$\frac{I_{0}}{2}$
B.$\frac{I_{0}}{4}$
C.$\frac{I_{0}}{8}$
D.$\frac{I_{0}}{16}$
Solution
$$\begin{matrix} & I_{1} = I_{0}\cos^{2}\left( \frac{45}{2} \right) \\ & I_{2} = I_{1}\cos^{2}\left( 90 - \frac{45}{2} \right) \\ & \ = I_{0}\cos^{2}\left( \frac{45}{2} \right)\sin^{2}\left( \frac{45}{2} \right) \\ & \ = \frac{I_{0}}{4}\left( 4\cos^{2}\left( \frac{45}{2} \right)\sin^{2}\left( \frac{45}{2} \right) \right) \\ & \ = \frac{I_{0}}{4}\sin^{2}45^{\circ} = \frac{I_{0}}{8} \end{matrix}$$
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