The speed of light in a medium of refractive index 1.5 is ________.

Options

A. `1.5 xx 10^(8) m//s`
B. `3.0 xx 10^(8) m//s`
C. `2.0 xx 10^(8) m//s`
D. `1.2 xx 10^(8) m//s`

Answer

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 Definition of 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).
\[ n = \frac{c}{v} \]

2. **Rearrange the Formula:**
To find the speed of light in the medium (v), we can rearrange the formula:
\[ v = \frac{c}{n} \]

3. **Substitute the Known Values:**
We know:
- The speed of light in vacuum (c) is approximately \(3 \times 10^8\) meters per second.
- The refractive index (n) is given as 1.5.
Now, substitute these values into the rearranged formula:
\[ v = \frac{3 \times 10^8 \text{ m/s}}{1.5} \]

4. **Perform the Calculation:**
Now, we can calculate the speed of light in the medium:
\[ v = \frac{3 \times 10^8}{1.5} = 2 \times 10^8 \text{ m/s} \]

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

### Final Answer:
The speed of light in a medium of refractive index 1.5 is \(2 \times 10^8\) meters per second.

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