Question

Problem4 (10 marks) A rotating polari that the angle between the polarizer (transmission axis) polarizer is θ. Prove that the emergent light varies wi zer is placed between crossed polarizer and analyzer such d TA2 for the rotating Unpolarized light TA TA TA lo

Answer 1

When an unpolarized light passes through polarizer 1, with its transmission axis parallel to X axis, the emitted light from polarizer 1 will be along X-axis with intensity $I_1=I_0$. (from the figure, intensity of light emitted from 1st polarizer is $I_0$ )

This light then passes through 2nd polarizer whose transmission axis is making an angle $\theta$ with the X-axis. The intensity of light emitted from 2nd polarizer will be $I_2=I_o\cos^2 \theta$ .

The light then passes through 3rd polarizer (analyzer) whose transmission axis is along Y-axis,( angle between 2nd and 3rd polarizers is $(90\degree- \theta)$ ). Intensity of light emitted from the 3rd polarizer will be $I=I_2\cos^2(90\degree- \theta)$

$I=I_0\cos^2\theta\cos^2(90\degree- \theta)=I_0\cos^2\theta\sin^2\theta$ ( since $\cos(90\degree-\theta)=\sin\theta$ )

$I=I_0(\sin\theta\cos\theta)^2=\frac{I_0}{4}(2\sin\theta\cos\theta)^2=\frac{I_0}{4}(\sin2\theta)^2=\frac{I_0}{4}\sin^22\theta$

Intensity of emergent light is $I=\frac{I_0}{4}\sin^22\theta$