Question

A beam of light of intensity \(I_0\) falls on a system of three polaroids such that each pass axis is turned through \(60^{\circ}\) with respect to preceding one. The fraction of intensity that passes through is:

• A. \(\frac{1}{8}\)
• B. \(\frac{1}{32}\)
• C. \(\frac{1}{16}\)
• D. \(\frac{1}{2}\)

Hint:

The first polaroid always cuts intensity by half; subsequent ones follow $\cos^2 \theta$.

Answer 1

The Correct Option is B

Step 1: First Polaroid
Unpolarized light $I_0$ passing through the first polaroid becomes $I_1 = \frac{I_0}{2}$.

Step 2: Malus's Law
$I = I_{incident} \cos^2 \theta$.
$I_2 = I_1 \cos^2 60^\circ = \frac{I_0}{2} (\frac{1}{2})^2 = \frac{I_0}{8}$.
$I_3 = I_2 \cos^2 60^\circ = \frac{I_0}{8} (\frac{1}{2})^2 = \frac{I_0}{32}$.

Step 3: Fraction
$\frac{I_3}{I_0} = \frac{1}{32}$.
Final Answer: (B)