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Wave Optics

Question
CBSEENPH12039084

a) Why are coherent sources necessary to produce a sustained interference pattern?

(b) In Young’s double slit experiment using monochromatic light of wavelength bold italic lambda , the intensity of light at a point on the screen where path difference is bold italic lambda is K units. Find out the intensity of light at a point where path difference is straight lambda over 3.

Solution

a)
Coherent sources have almost the same wavelength. Coherent sources are necessary to ensure that the positions of maxima and minima do not change with time. Thereby, producing a sustained interference pattern.
b)
Wavelength of monochromatic light = straight lambda
Path difference = bold lambda over bold 3 
So, phase difference, straight phi space equals space fraction numerator 2 straight pi over denominator straight lambda end fraction cross times straight lambda space equals space 2 straight space straight pi

Intensity of light = K units
Intensity is given by, I equals space straight I space equals space 4 space straight I subscript space 0 end subscript cos to the power of space 2 end exponent bevelled straight ϕ over 2
When path difference is bold italic lambda divided by 3, phase difference becomes straight phi straight space equals straight space fraction numerator 2 straight pi over denominator 3 end fraction
Intensity of light I’ = 4 space straight I subscript space 0 end subscript cos to the power of space 2 end exponent bevelled straight ϕ over 2 equals 4 space straight I subscript space 0 end subscript cos to the power of space 2 end exponent straight pi over 3 equals straight I subscript straight o
rightwards double arrow bold I apostrophe space equals space bold K over 4, is the new intensity of light.