What is the velocity of light in diamond approximately, If given that the index of refraction of diamond is 2.0.

Options

A. `1.5 xx 10^10cms^(- 1)`
B. `2 xx 10^(10) cms^(-1)`
C. `3.0 xx 10^(10) cms^(-1)`
D. `6 xx 10 ^(10) cms^(-1)`

Explanation

To find the velocity of light in diamond, we can use the relationship between the speed of light in a vacuum (or air) and the index of refraction of the material. The index of refraction (n) is defined as:

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

Where:
- \( n \) is the index of refraction,
- \( c \) is the speed of light in vacuum (approximately \( 3 \times 10^8 \) m/s),
- \( v \) is the speed of light in the medium (in this case, diamond).

Given that the index of refraction of diamond is \( n = 2.0 \), we can rearrange the formula to solve for \( v \):

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

Now, substituting the known values:

1. Substitute \( c = 3 \times 10^8 \) m/s and \( n = 2.0 \):

\[ v = \frac{3 \times 10^8 \, \text{m/s}}{2.0} \]

2. Perform the division:

\[ v = 1.5 \times 10^8 \, \text{m/s} \]

Thus, the velocity of light in diamond is approximately \( 1.5 \times 10^8 \) m/s.

To convert this into centimeters per second, we can use the conversion factor \( 1 \, \text{m} = 100 \, \text{cm} \):

3. Convert meters per second to centimeters per second:

\[ v = 1.5 \times 10^8 \, \text{m/s} \times 100 \, \text{cm/m} = 1.5 \times 10^{10} \, \text{cm/s} \]

Therefore, the final answer is:

**The velocity of light in diamond is approximately \( 1.5 \times 10^{10} \) cm/s.**