If the refractive index of diamond is 2.4 find the velocity of light in diamond.(c=`3xx10^(8)`m/s)

Options

A. `1.25xx10^(8)`m/s
B. `2.25xx10^(8)` m/s
C. `1.5xx10^(8)` m/s
D. `4.5xx10^(8)` m/s

Explanation

To find the velocity of light in diamond given its refractive index, we can follow these steps:

### Step 1: Write down the formula for 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 that medium (v). The formula is given by:
\[ n = \frac{c}{v} \]

### Step 2: Rearrange the formula to find the velocity of light in the medium
To find the velocity of light in diamond (v), we can rearrange the formula:
\[ v = \frac{c}{n} \]

### Step 3: Substitute the known values
We know:
- The speed of light in vacuum, \( c = 3 \times 10^8 \, \text{m/s} \)
- The refractive index of diamond, \( n = 2.4 \)

Now, substituting these values into the rearranged formula:
\[ v = \frac{3 \times 10^8 \, \text{m/s}}{2.4} \]

### Step 4: Perform the calculation
Now we perform the division:
\[ v = \frac{3 \times 10^8}{2.4} \]
Calculating this gives:
\[ v = 1.25 \times 10^8 \, \text{m/s} \]

### Final Answer
The velocity of light in diamond is:
\[ v \approx 1.25 \times 10^8 \, \text{m/s} \]

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