Question

An unpolarised beam of light is made to incident on an arrangement of four polarsing sheets arranged in such a way that the characteristic direction of each polarizing sheet makes an angle of ${45}^{\circ }$ with that of preceding sheet. What fraction of incident unpolarised light will be transmitted finally?

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{1}{8}$
• D. $\frac{1}{16}$

Answer 1

The correct option is D $\frac{1}{16}$

The intensity $I$ of light after passing through a polarizing filter is $I=I_{0}co{s}^2\theta$,
where $I_0$ is the original intensity and $\theta$ is the angle between the direction of polarization and the axis of the filter.

Intensity of light transmitted from $1^{st}$ polarizing sheet $I_1=I_{0}co{s}^2{45}^{\circ }=\frac{I_0}{2}$

Intensity of light transmitted from $2^{nd}$ sheet $I_2=\frac{I_0}{2}co{s}^2{45}^{\circ }=\frac{I_0}{4}$

Intensity of light transmitted from $3^{rd}sheet{I}_3=\frac{I_0}{4}co{s}^2{45}^{\circ }=\frac{I_0}{8}$

Intensity of final transmitted light from last sheet $I_4=\frac{I_0}{8}co{s}^2{45}^{\circ }=\frac{I_0}{16}$