Question 62: Wave Optics

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.

Accepted Answer

When light travels from one medium to another, its frequency remains constant, but its velocity and wavelength change.
The absolute refractive index is defined as:
$$ \mu=\frac{c}{v}=\frac{\lambda_{	ext {vacuum }}}{\lambda_{	ext {medium }}} $$
Therefore, for any two media, the product of the refractive index and the wavelength is constant:
$$ \mu_1 \lambda_1=\mu_2 \lambda_2 $$
Wavelength in water, $\lambda_1=540 \mathrm{~nm}$
Refractive index of water, $\mu_1=4 / 3$
Refractive index of the second medium, $\mu_2=3 / 2$
Using the relation $\mu_1 \lambda_1=\mu_2 \lambda_2$,
$$ \lambda_2=\frac{\mu_1 \lambda_1}{\mu_2} $$
$$\Rightarrow $$ $$ \lambda_2=\frac{\frac{4}{3} 	imes 540}{3 / 2}=\frac{4 	imes 540 	imes 2}{3 	imes 3}=480 \mathrm{~nm} $$
Therefore, the wavelength of the light in the second transparent medium is 480 nm .
Hence, the correct option is (C).

Answer

540

Answer

840

Answer

480

Answer

380

Wave Optics

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.

Choose the correct answer: