Question

If the wavelength of the light is reduced to one half, then the amount of scattering is:
(A) Increased by $16$ times
(B) Decreased by $16$ times
(C) Increased by $256$ times
(D) Decreased by $256$ times

Answer 1

The relation between the amount of scattering is inversely proportional to fourth power of the wavelength of the light. By using this relation we can determine the amount of scattering of light whose wavelength is reduced to half.

Complete step by step solution:
Wavelength of light: It is defined as the distance between identical points in the adjacent cycles of the waveform along a wire or space.
When the scattering particles have much smaller wavelength than the wavelength of light then the scattering is known as Rayleigh scattering. It states that the amount of scattering of light is inversely proportional to the fourth power of the wavelength of the light. The relation is as
Amount of scattering of light $\alpha \dfrac{1}{{{\lambda ^4}}}$ , where $\lambda$ is the wavelength of the waveform.
Now here in the question we are given that if the wavelength of the light is reduced to one half. So let us say the wavelength was initially ${\lambda _1}$ and when it gets reduced to half then wavelength ${\lambda _2} = \dfrac{{{\lambda _1}}}{2}$ .
And we know that the relation between scattering of light and wavelength so by using that relation if scattering initial wavelength was ${S_1}$ and scattering by final wavelength is ${S_2}$ then $\dfrac{{{S_2}}}{{{S_1}}} = {(\dfrac{{{\lambda _1}}}{{{\lambda _2}}})^4}$ Which means $\dfrac{{{S_2}}}{{{S_1}}} = {(\dfrac{1}{{\dfrac{1}{2}}})^4} = {2^4} = 16$ . Hence, if the wavelength of the light is reduced to one half, then the amount of scattering is increased by $16$ times.
So option A is correct.

Note:
Scattering of light: When light passes from one medium to another medium then a part of light is absorbed by the particles of the medium, this phenomenon is known as scattering of light.