In a young 's double slit experiment, a glass plate of refractive index 1.5 and thickness `5 times 10^-4` cm is kept in the path of one of the light rays. Then

Options

A. There will be no shift in the interference pattern
B. The fringe width will increases
C. The fringe width will decreases
D. The optical path of the ray will increases by `2.5 times 10^-4 cm`

Answer

To solve the problem regarding the Young's double slit experiment with a glass plate, we will follow these steps:

### Step 1: Understand the Problem
In the Young's double slit experiment, we have two light rays coming from two slits. When a glass plate is introduced in the path of one of the rays, it affects the optical path length of that ray.

### Step 2: Identify Given Values
- Refractive index of the glass plate, \( \mu = 1.5 \)
- Thickness of the glass plate, \( t = 5 \times 10^{-4} \) cm

### Step 3: Calculate the Increase in Optical Path Length
The increase in optical path length due to the glass plate can be calculated using the formula:
\[ \Delta L = (\mu - 1) \cdot t \]

### Step 4: Substitute the Values
Substituting the given values into the formula:
\[ \Delta L = (1.5 - 1) \cdot (5 \times 10^{-4} \text{ cm}) \]
\[ \Delta L = 0.5 \cdot (5 \times 10^{-4} \text{ cm}) \]
\[ \Delta L = 2.5 \times 10^{-4} \text{ cm} \]

### Step 5: Analyze the Effect on Interference Pattern
The introduction of the glass plate increases the optical path length of one of the rays by \( 2.5 \times 10^{-4} \) cm. This means that the interference pattern will shift. However, the fringe width remains unchanged as it depends on the wavelength and the distance between the slits.

### Step 6: Conclusion
The optical path of the ray is increased by \( 2.5 \times 10^{-4} \) cm, which results in a shift in the interference pattern. Therefore, the correct option regarding the effect of the glass plate on the interference pattern is that there will be a shift.

### Final Answer
The optical path increases by \( 2.5 \times 10^{-4} \) cm, leading to a shift in the interference pattern.

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