Light enters from air to diamond with refractive index 2.42 What is the speed of light in diamond ? Given, speed light in air is `3xx10^8ms^(-1)`.

Options

A. `1.24xx10^5ms^(-1)`
B. `1.24xx10^8ms^(-1)`
C. `1.08xx10^8ms^(-1)`
D. None of these

Answer

To find the speed of light in diamond, we can use the relationship between the speed of light in a medium and its refractive index. The refractive index (n) is defined as:

\[ n = \frac{c}{v} \]

where:
- \( n \) is the refractive index of the medium,
- \( c \) is the speed of light in a vacuum (or air, approximately),
- \( v \) is the speed of light in the medium.

Given:
- The refractive index of diamond, \( n = 2.42 \)
- The speed of light in air, \( c = 3 \times 10^8 \, \text{m/s} \)

We need to find the speed of light in diamond, denoted as \( v_d \).

### Step 1: Rearranging the formula
From the refractive index formula, we can rearrange it to solve for \( v_d \):

\[ v_d = \frac{c}{n} \]

### Step 2: Substituting the known values
Now we substitute the known values into the equation:

\[ v_d = \frac{3 \times 10^8 \, \text{m/s}}{2.42} \]

### Step 3: Performing the calculation
Now we perform the division:

\[ v_d = \frac{3 \times 10^8}{2.42} \]

Calculating this gives:

\[ v_d \approx 1.24 \times 10^8 \, \text{m/s} \]

### Final Answer
Thus, the speed of light in diamond is approximately:

\[ v_d \approx 1.24 \times 10^8 \, \text{m/s} \]

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