Question

Unpolarized light passes through two polaroids, the axis of one is vertical and that of the other is ${30}^o$ to the vertical. What is the orientation and intensity of the transmitted light?

• A. Plane polarized at ${60}^o$ to the vertical and having intensity $\frac{l_0}{4}$
• B. Plane polarized at ${30}^o$ to the vertical and having intensity of $\frac{3l_0}{8}$
• C. Plane polarized at ${30}^o$ to the vertical and having intensity $\frac{l_0}{2}$
• D. No light passes

Answer 1

Answer: (B)

Plane polarized at ${30}^o$ to the vertical and having intensity of $\frac{3l_0}{8}$

The first Polaroid alinsisates half the light so that the intensity is reduced by hail $I^{\prime }=\frac{I_0}{2}$. The light reaching the second polariser is vertically polarised and so intensity is reduced to $I^{\prime \prime }=I^{\prime }(cos{30}^o{)}^2=\left(\frac{3}{4}\right)\left(\frac{I_0}{2}\right)$
$=\frac{3I_0}{8}$
Therefore. transmitted light is plane polarised to the vertical at 30 and having intensity $=\frac{3I_0}{8}$.