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Wave Optics

Question
CBSEENPH12039782

The intensity at the maximum in a Young's double slit experiment is Io. Distance between two slits is d = 5 straight lambda, where straight lambda is the wavelength of light used in the experiment. What will be the intensity infront  of one of the slits on the screen placed at a distance D = 10 d?

  • straight I subscript straight o over 4
  • 3straight I subscript straight o over 4

  • straight I subscript straight o over 2
  • Io

Solution

C.

straight I subscript straight o over 2
In the fig., S1 and S2 are the two different slits.
Given, distances between slits S1 and S2
d = 5 straight lambda
Distance between the screen and slits, D = 10 d = 50 straight lambda
straight lambda is the wavelength of the light used in the experiment.
In Young's double slit experiment, the maximum intensity is Io.
rightwards double arrow space straight I subscript max space equals space straight I subscript straight o
Path difference, dY subscript straight n over straight D equals fraction numerator d x begin display style d over 2 end style over denominator 10 space d end fraction equals d over 20 equals lambda over 4
space space space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket space d space equals space 5 lambda right square bracket
Path difference of straight lambda corresponds to phase difference 2straight pi.
So, for path difference straight lambda over 4, phase difference is
straight ϕ space equals space fraction numerator 2 straight pi over denominator straight lambda end fraction straight x straight lambda over 4 equals straight pi over 2 equals 90 to the power of straight o
We know,
I = Io cos2 90 to the power of straight o over 2
space space space space space space straight I space equals space straight I subscript straight o space straight x open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses squared
rightwards double arrow space straight I space equals space straight I subscript straight o over 2