The angle between the axes of a polariser and an analyser is $45^{\circ}$. If the intensity of the…
The angle between the axes of a polariser and an analyser is $45^{\circ}$. If the intensity of the unpolarized light incident on the polariser is 1 , then the intensity of the light emerged from the analyser is
2 I
$\frac{\mathrm{I}}{2}$
I
$\frac{I}{4}$
Solution
The intensity of light after passing through polariser is $\mathrm{I}_1=\frac{\mathrm{I}}{2}$ The intensity of light after passing through analyses is
$I_2=I_1 \cos ^2 \theta=\frac{I}{2} \cos ^2 45^{\circ}=\frac{I}{2} \times\left(\frac{1}{\sqrt{2}}\right)^2=\frac{I}{4}$