Question

When particles scattering light are much smaller than its wavelength, the amount of scattering is proportional to 1/λ⁴. Does this mean there is more scattering for small λ than large λ? How does this relate to the fact that the sky is blue?

a) Yes, more scattering for small λ; blue sky results from shorter wavelengths.

b) No, less scattering for small λ; blue sky results from longer wavelengths.

c) Yes, more scattering for large λ; blue sky results from shorter wavelengths.

d) No, less scattering for large λ; blue sky results from longer wavelengths.

Answer 1

Scattering is inversely proportional to the fourth power of the wavelength, leading to more scattering for smaller, shorter wavelengths such as blue.

This Rayleigh scattering is why the sky appears blue, as the shorter blue light is scattered more throughout the atmosphere than longer wavelengths.

Therefore, the correct answer to the question is: a) Yes, more scattering for small λ; blue sky results from shorter wavelengths.

Step-by-step explanation:

When particles scattering light are much smaller than its wavelength, the scattering is inversely proportional to the fourth power of the wavelength (λ). T

his implies that there is indeed more scattering for small λ than for large λ. As a result, shorter wavelengths, like blue light, scatter more than longer wavelengths, such as red light, due to this Rayleigh scattering.

This principle is why the sky appears blue to us during the day. Sunlight entering the Earth's atmosphere encounters nitrogen and oxygen molecules, which are much smaller than the wavelengths of visible light.

The smaller, shorter blue wavelengths scatter more extensively, dispersing blue light all over the sky, while the longer wavelengths pass through with less scattering.

Therefore, the correct answer to the question is: a) Yes, more scattering for small λ; blue sky results from shorter wavelengths.