Chapter 18, Problem 43A

To determine

To Calculate: The speed of light in diamond.

Answer to Problem 43A

  $v=1.24\times {10}^8\text{m/s}$

Explanation of Solution

Given:

Speed of light in vacuum, $c=3\times {10}^8\text{m/s}$ (known value)

Refractive index of diamond, $\mu =2.42$

Formula used:

Refractive index of the medium can be obtained by:

  $\mu =\frac{c}{v}$

Here, c is the speed of light in vacuum and v is the speed of light in the medium.

Calculations:

Re-arrange the formula and solve for speed of light in diamond.

  $\begin{array}{c}v=\frac{c}{\mu }\\ =\frac{3\times {10}^8\text{m/s}}{2.42}\\ =1.24\times {10}^8\text{m/s}\end{array}$

Conclusion:

Thus, the speed of light in diamond is $v=1.24\times {10}^8\text{m/s}$ .