Question

The index of refraction of water is $\mathbf{1}\mathbf{.}\mathbf{33}$. At what speed would a wave crest in a beam of light travel through this medium?

Short answer

The speed of wave in the water is $2.25\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$.

Step-by-step solution

Identification of given data

The index of the refraction,$n=1.33$

Determine the formulas to calculate the speed of wave in the water.

The expression to calculate the speed of wave in the water is given as follows.

$\mathit{v}\mathbf{=}\frac{\mathbf{c}}{\mathbf{n}}$ …(i)

Here, c is the speed of the light.

Determining the speed of wave in the water.

Calculate the speed of wave in water.

Substitute $1.33forn$and $3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.forc$into equation (i).

$$\begin{gathered} v=\frac{3\times {10}^{8}m/s }{1.33} \\ v=2.25\times {10}^{8}m/s \end{gathered}$$

Hence the speed of wave in the water is $2.25\times {10}^{8}m/s$.