Two Nicols are oriented with their principal planes making an angle of `60^@`. The percentage of incident unpolarised light which passes through the system is

Options

A. (a) 50%
B. (b) 100%
C. (c) 12.5%
D. (d) 37.5%

Explanation

To solve the problem of finding the percentage of incident unpolarized light that passes through two Nicol prisms oriented at an angle of \(60^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Unpolarized Light**:
Unpolarized light consists of waves vibrating in all possible directions perpendicular to the direction of propagation. When it passes through a polarizer, only the component of light aligned with the polarizer's axis is transmitted.

2. **First Polarizer**:
When unpolarized light passes through the first Nicol (polarizer), the intensity of the transmitted light is given by:
\[ I_1 = \frac{I_0}{2} \]
where \(I_0\) is the intensity of the incident unpolarized light. This is because a polarizer transmits half of the incident unpolarized light.

3. **Intensity After First Polarizer**:
If we assume \(I_0 = 100\) (for simplicity), then:
\[ I_1 = \frac{100}{2} = 50 \]

4. **Second Polarizer**:
The second Nicol is oriented at an angle of \(60^\circ\) with respect to the first polarizer. The intensity of the light transmitted through the second polarizer is given by Malus's Law:
\[ I_2 = I_1 \cos^2(\theta) \]
where \(\theta\) is the angle between the two polarizers.

5. **Calculating Intensity After Second Polarizer**:
Substituting the values:
\[ I_2 = 50 \cos^2(60^\circ) \]
We know that \(\cos(60^\circ) = \frac{1}{2}\), so:
\[ I_2 = 50 \left(\frac{1}{2}\right)^2 = 50 \times \frac{1}{4} = 12.5 \]

6. **Calculating Percentage**:
To find the percentage of the incident unpolarized light that passes through the system, we calculate:
\[ \text{Percentage} = \left(\frac{I_2}{I_0}\right) \times 100 = \left(\frac{12.5}{100}\right) \times 100 = 12.5\% \]

### Final Answer:
The percentage of incident unpolarized light which passes through the system is **12.5%**.