Chapter 18, Problem 50A

To determine

The speed of violet and red light in float glass.

Answer to Problem 50A

  $1.96\times {10}^8\text{m/s}$ and $1.98\times {10}^8\text{m/s}$ , respectively.

Explanation of Solution

Given:

The index of refraction of float glass for violet light, $n_v=1.53$ .

The index of refraction of float glass for red light, $n_r=1.51$ .

Formula used:

The index of refraction is given by,

  $n=\frac{c}{v}$

Where,

  $\begin{array}{l}c=\text{ speed of light in vacuum}=3\times {10}^8\text{m/s}\\ v=\text{ speed of light in the medium}\end{array}$

Calculation:

Using the above formula, the speed of violet light in float glass will be,

  $\begin{array}{c}{n}_v=\frac{c}{v_v}\\ 1.53=\frac{3\times {10}^8}{v_v}\\ v_v=1.96\times {10}^8\text{m/s}\end{array}$

Similarly, the speed of red light in float glass will be,

  $\begin{array}{c}{n}_r=\frac{c}{v_r}\\ 1.51=\frac{3\times {10}^8}{v_r}\\ v_r=1.98\times {10}^8\text{m/s}\end{array}$

Conclusion:

Hence, the speed of violet light in float glass is $1.96\times {10}^8\text{m/s}$ and the speed of red light in float glass is $1.98\times {10}^8\text{m/s}$ .