Question

When monochromatic light travels from one medium to another, its wavelength changes but frequency remains the same Explain.

Answer 1

Hint: We are going to use two expressions in order to answer this question. One is the relation between the energy of the energy of a photon and the frequency. The other one is the relation between the velocity and the frequency. Frequency can be defined as the total number of waves that can pass a fixed point.

Complete step by step solution:
The relationship between the frequency and the energy is given by,
\[E = h\nu \]
Here \[E\] is the energy of the photon.
\[h\] is the Planck’s constant
 \[\nu \] is the frequency
If a light ray is passing from one medium to another medium then there will be no change in the energy. Then from the above equation, we can say that the frequency will also not change.
Similarly, we have another relationship,
\[v = f \times \lambda \]
Here \[v\] is the velocity of the wave. Here when the velocity of the wave changes the wavelength will also change. So to compensate for this change the frequency remains constant. From the above equation, frequency is equal to the ratio of the wavelength and velocity. Whenever light passes from one medium to another medium this ratio will always remain constant. Because both velocity and wavelength changes will compensate each other to give the final ratio equal for both mediums. Hence we can say that there will be no change in the frequency. The frequency will remain constant.

Note:
The two characteristics that will remain constant when the light passes from one medium to another are the energy of the photon and the frequency. As we already said this can be explained by Planck’s formula. This is because photons cannot be split into pieces and therefore the energy remains constant and hence the frequency remains constant.