In Fresnel's biprism experiment, on increasing the prism angle, the fringe width will

Options

A. (a) Increase
B. (b) Decrease
C. (c) Remain unchanged
D. (d) Depend on the position of object

Explanation

To solve the question regarding the effect of increasing the prism angle on the fringe width in Fresnel's biprism experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**:
The fringe width (β) in Fresnel's biprism experiment is given by the formula:
\[ \beta = \frac{(a + b) \lambda}{2a(\mu - 1) \alpha} \]
where:
- \( a \) = distance from the source to the prism
- \( b \) = distance from the prism to the screen
- \( \lambda \) = wavelength of light used
- \( \mu \) = refractive index of the prism
- \( \alpha \) = angle of the prism

2. **Identify the Relationship**:
From the formula, we can see that fringe width (β) is inversely proportional to the angle of the prism (α):
\[ \beta \propto \frac{1}{\alpha} \]

3. **Analyze the Effect of Increasing the Angle**:
If we increase the angle \( \alpha \), the denominator of the formula increases. Since β is inversely proportional to α, this means that as α increases, β will decrease.

4. **Conclusion**:
Therefore, when the prism angle is increased, the fringe width will decrease.

### Final Answer:
On increasing the prism angle in Fresnel's biprism experiment, the fringe width will **decrease**.

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