Two light sources can be adjusted to emit monochromatic light of any visible wavelength. the two sources are coherent, 2.04μm apart, and in line with an observer, so that one source is 2.04μm farther from the observer than the other.

part a

for what visible wavelengths (400 to 700 nm) will the observer see the brightest light, owing to constructive interference?

part b

what would your answers to part (a) be if the two sources were not in line with the observer, but were still arranged so that one source is 2.04μm farther away from the observer than the other?

part c

for what visible wavelengths will there be destructive interference at the location of the observer?

Explanation:

Path difference for the observer = 2.04μm

For constructive interference

path difference = n λ

2.04μm =  5 x .408 or , 4 x .51 or 3 x .68μm

 For  visible wavelengths like .408 , .51 or .68 μm  (400 to 700 nm) will the observer see the brightest light due to constructive interference.

B)  If the two sources were not in line with the observer, but were still arranged so that one source is 2.04μm farther away from the observer than the other , in that case also , interference pattern will be visible .

c )

For destructive interference

2.04 μm  = (2n+1)λ / 2

2.04μm = 3.5 x .58μm

2.04 μm = 4.5 x .45μm

So for  .58μm and .45μm , destructive interference will take place

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.