A beam of unpolarized light of intensity $I$ passes through two polarizers. The first polarizer has its transmission axis at $30^{\circ }$ to the vertical, and the second has its axis at $60^{\circ }$ to the vertical. What is the intensity of the light emerging from the second polarizer?

Solution

1. When unpolarized light of intensity $I$ passes through the first polarizer, the emerging intensity is $I_1=I/2$.
2. The angle between the transmission axes of the two polarizers is $$\begin{array}{rl}\theta & =60^{\circ }-30^{\circ }\\ & =30^{\circ }\end{array}$$.
3. Applying Malus's Law, the final intensity is $$\begin{array}{rl}{I}_2& =I_1{\cos }^2(30^{\circ })\\ & =(I/2)\times (\sqrt{3}/2{)}^2\end{array}$$.
4. Calculating the final value gives $$\begin{array}{rl}{I}_2& =(I/2)\times (3/4)\\ & =3I/8\end{array}$$.
5. Hence the answer is (D).