Two nicol prisms are inclined to each other at an angle `30^(@)`. If I is the intensity of ordinary light incident on the first prism, then the intensity of light emerges from the second prism will be

Options

A. `3I"/"4`
B. `I"/"2`
C. `I"/"4`
D. `3I"/"8`

Answer

To solve the problem of finding the intensity of light emerging from the second Nicol prism when two prisms are inclined at an angle of \(30^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have two Nicol prisms, and ordinary light of intensity \(I\) is incident on the first prism. We need to find the intensity of light \(I_0\) that emerges from the second prism after passing through the first.

2. **Use the Intensity Relation**: The relationship between the intensity of the incident light \(I\) and the emerging light \(I_0\) after passing through a Nicol prism inclined at an angle \(\theta\) is given by:
\[ \frac{I_0}{I} = \frac{1}{2} \cos^2 \theta \]

3. **Substitute the Angle**: In our case, the angle \(\theta\) is \(30^\circ\). Therefore, we substitute \(\theta\) into the equation:
\[ \frac{I_0}{I} = \frac{1}{2} \cos^2(30^\circ) \]

4. **Calculate \(\cos(30^\circ)\)**: We know that:
\[ \cos(30^\circ) = \frac{\sqrt{3}}{2} \]
Thus,
\[ \cos^2(30^\circ) = \left(\frac{\sqrt{3}}{2}\right)^2 = \frac{3}{4} \]

5. **Substitute Back into the Intensity Relation**: Now we substitute \(\cos^2(30^\circ)\) back into the intensity equation:
\[ \frac{I_0}{I} = \frac{1}{2} \cdot \frac{3}{4} = \frac{3}{8} \]

6. **Find the Emerging Intensity**: Now, we can express \(I_0\) in terms of \(I\):
\[ I_0 = I \cdot \frac{3}{8} \]

7. **Final Result**: Therefore, the intensity of light emerging from the second Nicol prism is:
\[ I_0 = \frac{3I}{8} \]

### Conclusion:
The intensity of light that emerges from the second Nicol prism is \(\frac{3I}{8}\).

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