Question

In the figure, initially unpolarized light is sent into a system of three polarizing sheets whose polarizing directions make angles of${\mathbf{\theta }}_1\mathbf{=}{\mathbf{\theta }}_2\mathbf{=}{\mathbf{\theta }}_3\mathbf{=}\text{50°}$with the direction of theyaxis. What percentage of the initial intensity is transmitted by the system? (Hint: Be careful with the angles.)

Figure:

Short answer

The intensity of light after the third polarizer is$I_f=0.045\%I_0$

Step-by-step solution

Given

${\theta }_1={\theta }_2={\theta }_3={50}^0$

Determining the concept

According to Malus law, the intensity of a beam of plane-polarized light after passing through a rotatable polarizer varies as the square of the cosine of the angle through which the polarizer is rotated from the position that gives maximum intensity.

Determining the percentage of the initial intensity is transmitted by the system

The intensity of light after the third polarizer is:

$\begin{array}{l}{I}_f=\frac{I_0}{2}({\theta }_1+{\theta }_2)({\theta }_2+{\theta }_3)\\ I_f=0.5\times (50+50)(50+50)\\ \frac{I_f}{I_0}=4.5\times {10}^{-4}\\ \therefore I_f=0.045\%I_0\end{array}$

Hence, the intensity of light after the third polarizer is$I_f=0.045\%I_0$.