You can determine the index of refraction of a substance by determining its critical angle. (a) what is the index of refraction of a substance that has a critical angle of 47.3â° when submerged in ethanol, which has an index of refraction of 1.361? (b) what would the critical angle be for this substance in air?

a )1.851

b ) 32.68°

Explanation:

The relation between critical angle and index of refraction is as follows

Sin C = 1 / μ

C is critical angle and μ is refractive index.

Given C = 47.3

Sin 47.3 = 1 / μ

0.735 = 1 / μ

μ = 1 / .735

= 1.36

This is with respect to ethanol .

1.36 = refractive index of material /  refractive index of ethanol

refractive index of material = 1.36 x refractive index of ethanol

= 1.36 x 1.361 = 1.851

If critical angle for this substance be A

Sin A = 1 / 1.851 = .54

A = 32.68° .

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.