The wavelength of light, while it is passing through water is 540 nm . The refractive index of water

Question

The wavelength of light, while it is passing through water is 540 nm . The refractive index of water is $4 / 3$. The wavelength of the same light when it is passing through a transparent medium having refractive index of $3 / 2$ is $\_\_\_\_$ nm.

Professor PC Thomas Classes · Answer

The wavelength of light in a medium is inversely proportional to its refractive index, $\lambda \propto \frac{1}{\mu}$. Thus, $\lambda_m \mu_m = \lambda_w \mu_w$. Substituting the given values: $\lambda_m 	imes \frac{3}{2} = 540 	imes \frac{4}{3}$. This gives $\lambda_m 	imes \frac{3}{2} = 720 \Rightarrow \lambda_m = 720 	imes \frac{2}{3} = 480 	ext{ nm}$.