The wavelength of yellow sodium light in air is 589 nm. (a) What is its frequency? (b) What is its wavelength in glass whose index of refraction is 1.52? (c) From the results of (a) and (b), find its speed in this glass.

The wavelength of yellow sodium light in air is $\lambda =589\text{nm}$.

The index of refraction of glass is,$n=1.52$.

The frequency of a wave can be calculated mathematically by dividing the value of the wavelength from the speed of light.

So, if the wavelength increases then the value of frequency of the wave decreases accordingly.

The formula for the frequency of yellow sodium light is given by,

$f=\frac{c}{\lambda }$

Here, speed of light$c=3\times {10}^8\text{m/s}$

Putting the values,

$$\begin{gathered} f=\frac{3\times {10}^8\text{m/s}}{589\times {10}^{-9}\text{m}} \\ f=5.09\times {10}^{14}\text{Hz} \end{gathered}$$

Hence, the frequency of yellow sodium light is$5.09\times {10}^{14}\text{Hz}$

The formula for the wavelength of the light when traveling through the glass is given by,

$$\begin{gathered} {\lambda }_n=\frac{\lambda }{n} \\ {\lambda }_n=\frac{589\text{nm}}{1.52} \\ {\lambda }_n=387.5\text{nm} \end{gathered}$$

Hence, the wavelength of the light when traveling through the glass is$387.5\text{nm}$

The formula for the light speed when traveling through the glass is given by,

$v=f{\lambda }_n$

Putting values of $f$ and ${\lambda }_n$,

$$\begin{gathered} v=5.09\times {10}^{14}\text{Hz}\times 387.5\times {10}^{-9}\text{m} \\ v=1.97\times {10}^8\text{m/s} \end{gathered}$$

Hence, the light speed when traveling through the glass is$1.97\times {10}^8\text{m/s}$