Suppose you are using total internal reflection to make an efficient corner reflector (see section 7). if there is air outside and the incident angle is 45.0º, what must be the minimum index of refraction of the material from which the reflector is made?

1.414

Explanation:

the critical angle is the minimum angle of incidence in the denser medium for which the angle of refraction in rarer medium is 90 degree.

the relation between the refractive index and critical angle is given by

n = 1 / Sin i

n = 1 / Sin 45

n = 1.414

thus, the refractive index of the material medium is 1.414.

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.