Question

'n' polarizing sheets are arranged such that each makes an angle \(45^{\circ}\) with the preceding sheet. An unpolarized light of intensity \(I\) is incident into this arrangement. The output intensity is found to be \(I/64\). The value of \(n\) will be

• A. \(3\)
• B. \(6\)
• C. \(5\)
• D. \(4\)

Hint:

The first sheet halves the intensity; each next sheet multiplies by \(\cos^2 45^{\circ}=\frac12\).

Answer 1

The Correct Option is B

Step 1: Plan:
Follow the intensity through each sheet.

Step 2: Steps:
After sheet 1: $\frac I2$. After sheet 2: $\frac I4$. After sheet 3: $\frac I8$. The pattern is $\frac{I}{2^k}$ after sheet $k$. We need $\frac{I}{64}$, which is $\frac{I}{2^6}$, so $k = 6$.

Final Answer:
The number of sheets is $6$, option (B). \[ \boxed{6} \]