The speed of light in a homogeneous medium of refractive index `(5)/(4)` is

Options

A. `2.4 xx 10^(5) km//sec`
B. `2.4 xx 10^(5) m//s`
C. `2.4 xx 10^(8) cm//s`
D. All the above

Answer

To find the speed of light in a homogeneous medium with a refractive index of \( \frac{5}{4} \), we can use the formula that relates the speed of light in a vacuum (C) to the speed of light in a medium (V) through the refractive index (n):

\[ n = \frac{C}{V} \]

### Step-by-step Solution:

1. **Identify the given values**:
- Refractive index, \( n = \frac{5}{4} \)
- Speed of light in vacuum, \( C = 3 \times 10^8 \) m/s

2. **Rearrange the formula to solve for V**:
\[ V = \frac{C}{n} \]

3. **Substitute the known values into the equation**:
\[ V = \frac{3 \times 10^8 \text{ m/s}}{\frac{5}{4}} \]

4. **Simplify the fraction**:
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[ V = 3 \times 10^8 \text{ m/s} \times \frac{4}{5} \]

5. **Perform the multiplication**:
\[ V = \frac{12 \times 10^8}{5} \text{ m/s} \]

6. **Calculate the speed**:
\[ V = 2.4 \times 10^8 \text{ m/s} \]

7. **Convert to other units if necessary**:
- To convert to kilometers per second:
\[ V = 2.4 \times 10^8 \text{ m/s} = 2.4 \times 10^5 \text{ km/s} \]
- To convert to centimeters per second:
\[ V = 2.4 \times 10^8 \text{ m/s} = 2.4 \times 10^{10} \text{ cm/s} \]

### Final Answer:
The speed of light in the homogeneous medium is \( 2.4 \times 10^8 \) m/s, or \( 2.4 \times 10^5 \) km/s, or \( 2.4 \times 10^{10} \) cm/s.

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