A light wave enters from air into a medium of refractive index 1.5. The speed of light in the medium will be

Options

A. `2 xx 10^(8)m//s`
B. `4.5 xx 10^(8) m//s`
C. `9 xx 10^(8) m//s`
D. `(330//1.5) xx 10^(8) m//s`

Explanation

To find the speed of light in a medium with a refractive index of 1.5, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between speed of light and refractive index**:
The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v). This can be expressed as:
\[ n = \frac{c}{v} \]

2. **Rearranging the formula**:
From the above equation, we can rearrange it to find the speed of light in the medium:
\[ v = \frac{c}{n} \]

3. **Substituting known values**:
We know that the speed of light in vacuum (c) is approximately \(3 \times 10^8 \, \text{m/s}\) and the refractive index (n) of the medium is given as 1.5. Substituting these values into the equation gives:
\[ v = \frac{3 \times 10^8 \, \text{m/s}}{1.5} \]

4. **Calculating the speed**:
Performing the division:
\[ v = 3 \times 10^8 \div 1.5 = 2 \times 10^8 \, \text{m/s} \]

5. **Conclusion**:
Therefore, the speed of light in the medium with a refractive index of 1.5 is:
\[ v = 2 \times 10^8 \, \text{m/s} \]

### Final Answer:
The speed of light in the medium is \(2 \times 10^8 \, \text{m/s}\).

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