Two parallel rays are travelling in a medium of refractive index `mu_(1)=4//3`. One of the rays passes through a parallel glass slab of thickness t and refractive index `mu_(2)=3//2`. The path difference between the two rays due to the glass slab will be

Options

A. 4t/3
B. 3t/2
C. t/8
D. t/6

Answer

To find the path difference between two parallel rays when one ray passes through a glass slab, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Refractive index of the medium (before the slab), \( \mu_1 = \frac{4}{3} \)
- Refractive index of the glass slab, \( \mu_2 = \frac{3}{2} \)
- Thickness of the glass slab, \( t \)

2. **Understanding Path Difference:**
- When a ray of light passes through a medium with a different refractive index, it effectively travels a longer distance compared to a ray traveling in the original medium. This difference in distance is termed as path difference.

3. **Formula for Path Difference:**
- The path difference \( \Delta X \) due to the glass slab can be calculated using the formula:
\[ \Delta X = t \left( \frac{\mu_2}{\mu_1} - 1 \right) \]

4. **Substituting Values:**
- Substitute the values of \( \mu_1 \) and \( \mu_2 \) into the formula:
\[ \Delta X = t \left( \frac{3/2}{4/3} - 1 \right) \]

5. **Simplifying the Expression:**
- Calculate \( \frac{3/2}{4/3} \):
\[ \frac{3/2}{4/3} = \frac{3}{2} \times \frac{3}{4} = \frac{9}{8} \]
- Now substitute this back into the path difference formula:
\[ \Delta X = t \left( \frac{9}{8} - 1 \right) \]

6. **Further Simplification:**
- Calculate \( \frac{9}{8} - 1 \):
\[ \frac{9}{8} - 1 = \frac{9}{8} - \frac{8}{8} = \frac{1}{8} \]
- Thus, we have:
\[ \Delta X = t \cdot \frac{1}{8} \]

7. **Final Result:**
- Therefore, the path difference between the two rays due to the glass slab is:
\[ \Delta X = \frac{t}{8} \]

### Conclusion:
The path difference between the two rays due to the glass slab is \( \frac{t}{8} \).

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