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If the size of a particle is a and the wavelength of light is λ, then for a λ the scattering is directly proportional to ________.

Asked in GSEB Board March 2020 · Dispersion and scattering

Answer: (2) 1/(λ⁴)

Step-by-step solution

Given: scattering particles much smaller than the wavelength, a λ.

Idea: in this limit each particle is driven by the light's electric field as a tiny oscillating dipole, and the power radiated by such a dipole goes as the fourth power of its frequency.

Since u = c/λ, a fourth power of frequency is the same as an inverse fourth power of wavelength.

So the scattered intensity follows Rayleigh's law, scattering ∝ 1/(λ⁴).

This is why the sky is blue: the short wavelengths in sunlight are scattered out of the direct beam many times more strongly than the long ones.

Why the other options are wrong

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