Question

The color of the sky is due to the scattering of solar light by the molecules of the atmosphere. Lord Rayleigh was one of the first to study scattering of this kind. He showed that the amount of scattering for very small particles such as molecules is inversely proportional to the fourth power of the wavelength. Estimate the ratio of the scattering efficiency of light at the wavelength of the maximum for the "blue" cones, as compared with that for the "green" cones.

Answer 1

Rayleigh scattering indicates that blue light is scattered more efficiently than green light, leading to the blue appearance of the sky. The blue light scatters around 12 times more efficiently than green light.

Step-by-step explanation:

The scattering efficiency of light is inversely proportional to the fourth power of the wavelength, according to Rayleigh scattering. Since blue light has a shorter wavelength than green light, it scatters more efficiently. The wavelength of blue light that maximizes the response of the "blue" cones in our eyes is around 445 to 450 nm, and for "green" cones, it's around 535 nm. Using Rayleigh's law, the ratio of the scattering efficiency for blue versus green light would be (535/450)4, which is approximately 1.884 or around 12.5. This indicates that blue light is scattered over 12 times more efficiently than green light, contributing to the blue appearance of the sky.