Question

What will be the wavelength of a blue ray of light $\left( a=450\text{ nm} \right)$ be when it leaves air and goes into water which has an index of refraction of $1.33$.

Answer 1

To solve these types of questions, we must know the relation between the wavelength and the refractive index of the medium of a light ray that passes from air to water. We know that when a light ray travels from air to water, its speed decreases along with a slight change in its direction of propagation.

Complete step-by-step solution:
To solve this question first let us discuss the relationship between the wavelength of blue ray light with the refractive index of the medium. The wavelength $(\lambda )$ of the blue ray light is inversely proportional to the refractive index of the medium $(\mu )$ and the relation can be written as:
$\lambda \propto \dfrac{1}{\mu }$
Thus, the wavelength of the blue ray of light before and after passing from air to water can be written as follows:
$\dfrac{{{\lambda }_{water}}}{{{\lambda }_{air}}}=\dfrac{{{\mu }_{air}}}{{{\mu }_{water}}}$
On substituting the values in the equation, we get as follows:
$\begin{aligned} & \dfrac{{{\lambda }_{water}}}{450}=\dfrac{1}{1.33} \\\ & \Rightarrow {{\lambda }_{water}}=\dfrac{450}{1.33} \\\ & \therefore {{\lambda }_{water}}=338.35\text{ nm} \\\ \end{aligned}$
Thus, the wavelength of a blue ray of light when it leaves air and goes into water which has an index of refraction of $1.33$ will be $338.35\text{ nm}$. Therefore, we may observe that the wavelength of the blue light ray that passes from air to water decreases as compared to its initial value.
Note: We must remember that when a ray of light travels from a rarer medium to a denser medium then its wavelength decreases, also the velocity of the ray of light decreases. The opposite would happen when a ray of light travels from a denser medium to a rarer medium, for example from water to air.