Question

A light of wavelenght 400 nm passes from air to water. a. what is the frequency of light in water? b. What is the speed of light in water if its index of refraction is 1.33 ? c. What is the wavelength of light in water?

Answer 1

a) Let's first find the frequency of light in air:

$$f=\dfrac{c}{\lambda}=\dfrac{3\times10^8\ \dfrac{m}{s}}{400\times10^{-9}\ m}=7.5\times10^{14}\ Hz.$$

The frequency of light does not change when it passes from one medium to the other one, therefore, the frequency of light in water is $f_w=7.5\times10^{14}\ Hz$.

b) We can find the speed of light in water as follows:

$$v=\dfrac{c}{n}=\dfrac{3\times10^8\ \dfrac{m}{s}}{1.33}=2.25\times10^8\ \dfrac{m}{s}.$$

c) We can find the wavelength of light in water as follows:

$$\lambda_w=\dfrac{\lambda}{n}=\dfrac{400\times10^{-9}\ m}{1.33}=301\times10^{-9}\ m.$$