A beam of natural light falls on a system of 5 polaroids, which are arranged in succession such that the pass axis of each polaroid is turned through `60^(@)` with respect to the preceding one. The fraction of the incident light intensity that passes through the system is :

Options

A. 0.24
B. 0.16
C. 0.12
D. 0.32

Answer

To solve the problem of determining the fraction of incident light intensity that passes through a system of five polaroids arranged with their pass axes at 60 degrees to each other, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Condition**:
- We start with a beam of natural light, which can be considered as unpolarized light. The initial intensity of this light is denoted as \( I_0 \).

2. **First Polaroid**:
- When unpolarized light passes through the first polaroid, according to Malus's Law, the intensity of the transmitted light is reduced to half.
- Therefore, after the first polaroid, the intensity \( I_1 \) is given by:
\[ I_1 = \frac{I_0}{2} \]

3. **Subsequent Polaroids**:
- Each subsequent polaroid is oriented at an angle of 60 degrees with respect to the previous one. We will apply Malus's Law for each of the following polaroids.
- For the second polaroid:
\[ I_2 = I_1 \cos^2(60^\circ) = \frac{I_0}{2} \cdot \left(\frac{1}{2}\right) = \frac{I_0}{4} \]

4. **Continuing the Process**:
- For the third polaroid:
\[ I_3 = I_2 \cos^2(60^\circ) = \frac{I_0}{4} \cdot \left(\frac{1}{2}\right) = \frac{I_0}{8} \]
- For the fourth polaroid:
\[ I_4 = I_3 \cos^2(60^\circ) = \frac{I_0}{8} \cdot \left(\frac{1}{2}\right) = \frac{I_0}{16} \]
- For the fifth polaroid:
\[ I_5 = I_4 \cos^2(60^\circ) = \frac{I_0}{16} \cdot \left(\frac{1}{2}\right) = \frac{I_0}{32} \]

5. **Final Calculation**:
- After passing through all five polaroids, the final intensity \( I_5 \) is:
\[ I_5 = \frac{I_0}{32} \]
- To find the fraction of the incident light intensity that passes through the system, we calculate:
\[ \text{Fraction} = \frac{I_5}{I_0} = \frac{I_0/32}{I_0} = \frac{1}{32} \]

### Final Answer:
The fraction of the incident light intensity that passes through the system of five polaroids is \( \frac{1}{32} \).