Velocity of light in medium 1 is `2.4 xx 10^7 "m s"^(-1)` and velocity of light in medium 2 is `1.8 xx 10^7 "m s"^(-1)`, then the refractive index of medium 2 with respect to medium 1 is

Options

A. `3/4`
B. `4/3`
C. `1/3`
D. `1/4`

Answer

To find the refractive index of medium 2 with respect to medium 1, we can use the formula for refractive index, which is defined as the ratio of the velocities of light in the two media. The formula is given by:

\[ \text{Refractive Index} (\mu) = \frac{V_1}{V_2} \]

Where:
- \( V_1 \) is the velocity of light in medium 1
- \( V_2 \) is the velocity of light in medium 2

### Step-by-Step Solution:

1. **Identify the velocities**:
- Velocity of light in medium 1 (\( V_1 \)) = \( 2.4 \times 10^7 \, \text{m/s} \)
- Velocity of light in medium 2 (\( V_2 \)) = \( 1.8 \times 10^7 \, \text{m/s} \)

2. **Set up the formula for refractive index**:
\[ \mu_{2,1} = \frac{V_1}{V_2} \]

3. **Substitute the values into the formula**:
\[ \mu_{2,1} = \frac{2.4 \times 10^7}{1.8 \times 10^7} \]

4. **Simplify the expression**:
- The \( 10^7 \) in the numerator and denominator cancels out:
\[ \mu_{2,1} = \frac{2.4}{1.8} \]

5. **Perform the division**:
- To simplify \( \frac{2.4}{1.8} \), we can multiply both the numerator and denominator by 10 to eliminate the decimal:
\[ \mu_{2,1} = \frac{24}{18} \]

6. **Reduce the fraction**:
- Both 24 and 18 can be divided by 6:
\[ \mu_{2,1} = \frac{24 \div 6}{18 \div 6} = \frac{4}{3} \]

7. **Conclusion**:
- The refractive index of medium 2 with respect to medium 1 is:
\[ \mu_{2,1} = \frac{4}{3} \]

### Final Answer:
The refractive index of medium 2 with respect to medium 1 is \( \frac{4}{3} \).