Question

In above figure (1), unpolarized light is sent into a system of three polarizing sheets.The angles ${\theta }_1$, ${\theta }_2$ and ${\theta }_3$ of the polarizing directions are measured counterclockwise from the positive direction of the $y$ axis (they are not drawn to scale). Angles ${\theta }_1$ and ${\theta }_3$ are fixed, but angle ${\theta }_2$ can be varied. Above figure (2) gives the intensity of the light emerging from sheet 3 as a function of ${\theta }_2$. (The scale of the intensity axis is not indicated.) What percentage of the light’s initial intensity is transmitted by the system when ${\theta }_2={30}^0$?

Answer 1

We note the points at which the curve is zero ( ${\theta }_2=0^0$ and ${90}^0$) in figure (2).

We infer that sheet 2 is perpendicular to one of the other sheets at ${\theta }_2=0^0$,

and that it is perpendicular to the other of the other sheets when ${\theta }_2={90}^0$.

Without loss of generality,

we choose ${\theta }_1=0^0$, ${\theta }_3={90}^0$.

Now, when ${\theta }_2={30}^0$, it will be $\Delta \theta ={30}^0$ relative to sheet 1 and

$\Delta {\theta }^{\prime }={60}^0$ relative to sheet 3.

Therefore,

$\frac{I_f}{I_i}=\frac{1}{2}{\cos }^2\left(\Delta \theta \right){\cos }^2\left(\Delta {\theta }^{\prime }\right)=9.4$%.