Q5E - University Physics with Modern Physics

Question

A light beam travels at$\mathbf{1}\mathbf{.}\mathbf{94}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}\mathbf{m}\mathbf{/}\mathbf{s}$in quartz. The wavelength of the light in quartz is 355 nm. (a) What is the index of refraction of quartz at this wavelength? (b) If this same light travels through air, what is its wavelength there?

Step-by-Step Solution

Answer

1. The refractive index of quartz is 1.55 .
2. The wavelength in air is $5.50\times {10}^{-7}m$.

Step 1: (a) Determination of the refractive index of quartz.

The refractive index expression is given as,

$n=\frac{c}{v}$

  

Here, $c=3.00\times {10}^{8}m/s$  

So, the value of refractive index is,

$$\begin{gathered} n=\frac{3.00\times {10}^{8}m/s}{1.94\times {10}^{8}m/s} \\ =1.55 \end{gathered}$$ 

Step 2: (b) Determination of the wavelength of light in air.

The wavelength of light in quartz = 355 nm

The shift in wavelength is given as,

$\lambda =\frac{{\lambda }_0}{n}$ 

Thus, solve for the wavelength in air,

$$\begin{gathered} {\lambda }_0={\lambda }_n \\ =\left(1.55\right)\left(3.55\times {10}^{-7}m\right) \\ =5.50\times {10}^{-7}m \end{gathered}$$