Question

A beam of natural light falls on a system of $6$ Polaroids, which are arranged in succession such that each of the Polaroid is turned through ${30}^0$ with respect to the proceeding the one. The percentage of incident intensity that passes through the system will be:

• A. $100\%$
• B. $50\%$
• C. $30\%$
• D. $12\%$

Answer 1

The correct option is D $12\%$

Let $I_0$ be the intensity of incident light wave.

The incident wave oscillates in all directions. After passing through the first Polaroid, the intensity is the average of intensity of all waves emerging from the Polaroid, following Malus' Law.

Hence $I_1=I_0(co{s}^2\theta {)}_{avg}=\frac{I_0}{2}$

Now this wave is polarized in one direction. This now enters the second Polaroid to again follow Malus' Law with $\theta ={30}^{\circ }$

Hence, $I_2=\frac{I_0}{2}(\frac{\sqrt{3}}{2}{)}^2$

This occurs till the sixth Polaroid to get the final intensity $I_6$=$\frac{I_0}{2}(\frac{\sqrt{3}}{2}{)}^{10}$

Hence $\frac{I_6}{I_0}=12$%