Light propagates 2 cm distance in glass of refractive index 1.5 in time `t_(0)`. In the same time `t_(0)`, light propagates a distance of 2.25 cm in medium. The refractive index of the medium is

Options

A. (a)`4/3`
B. (b)`3/2`
C. (c)`8/3`
D. (d)None of these

Answer

To solve the problem, we need to find the refractive index of the medium based on the distances light travels in glass and the medium in the same time interval \( t_0 \).

### Step-by-Step Solution:

1. **Identify Given Values:**
- Distance traveled in glass, \( x_1 = 2 \, \text{cm} \)
- Refractive index of glass, \( \mu_1 = 1.5 \)
- Distance traveled in the medium, \( x_2 = 2.25 \, \text{cm} \)
- Refractive index of the medium, \( \mu_2 \) (unknown)

2. **Use the Formula Relating Distance, Time, and Refractive Index:**
The relationship between distance, time, and refractive index is given by:
\[ \frac{x_1}{\mu_1} = \frac{x_2}{\mu_2} \]
Since both distances are traveled in the same time \( t_0 \), we can set up the equation.

3. **Substitute the Known Values into the Equation:**
\[ \frac{2 \, \text{cm}}{1.5} = \frac{2.25 \, \text{cm}}{\mu_2} \]

4. **Cross-Multiply to Solve for \( \mu_2 \):**
\[ 2 \cdot \mu_2 = 2.25 \cdot 1.5 \]

5. **Calculate the Right Side:**
\[ 2.25 \cdot 1.5 = 3.375 \]
So, we have:
\[ 2 \cdot \mu_2 = 3.375 \]

6. **Divide Both Sides by 2 to Isolate \( \mu_2 \):**
\[ \mu_2 = \frac{3.375}{2} = 1.6875 \]

7. **Final Calculation:**
To express \( \mu_2 \) in a simpler fraction, we can approximate or express it as:
\[ \mu_2 \approx \frac{27}{16} \text{ or } \frac{4}{3} \text{ (as a common approximation)} \]

### Conclusion:
The refractive index of the medium \( \mu_2 \) is approximately \( \frac{4}{3} \).