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Wave Optics

Question
CBSEENPH12039949

Two slits in  Young's experiment have widths in the ratio 1:25.The ratio of intensity at the maxima and minima in the interference pattern Imax/Imin is

  • 9/4

  • 121/49

  • 49/121

  • 4/9

Solution

A.

9/4

Given, YDSE experiment, having two slits of width are in the ratio of 1:25
So, ratio of intensity

straight I subscript 1 over straight I subscript 2 space equals space straight W subscript 1 over straight W subscript 2 space equals space 1 over 25

rightwards double arrow space straight I subscript 2 over straight I subscript 1 space equals space 25 over 1
therefore comma
straight I subscript max over straight I subscript min space equals space fraction numerator left parenthesis square root of straight I subscript 2 end root space plus square root of straight I subscript 2 end root right parenthesis squared over denominator left parenthesis square root of straight I subscript 2 end root minus square root of straight I subscript 1 end root right parenthesis squared end fraction space equals space open square brackets fraction numerator square root of begin display style straight I subscript 2 over straight I subscript 1 end style end root plus 1 over denominator square root of straight I subscript 2 over straight I subscript 1 end root minus 1 end fraction close square brackets squared

rightwards double arrow space open square brackets fraction numerator 5 plus 1 over denominator 5 minus 1 end fraction close square brackets squared space equals space open parentheses 6 over 4 close parentheses squared space equals space 36 over 16 space equals space 9 over 4

Thus space straight I subscript max over straight I subscript min space equals space 9 over 4straight I subscript 1 over straight I subscript 2 space equals space straight W subscript 1 over straight W subscript 2 space equals space 1 over 25

rightwards double arrow space straight I subscript 2 over straight I subscript 1 space equals space 25 over 1
therefore comma
straight I subscript max over straight I subscript min space equals space fraction numerator left parenthesis square root of straight I subscript 2 end root space plus square root of straight I subscript 2 end root right parenthesis squared over denominator left parenthesis square root of straight I subscript 2 end root minus square root of straight I subscript 1 end root right parenthesis squared end fraction space equals space open square brackets fraction numerator square root of begin display style straight I subscript 2 over straight I subscript 1 end style end root plus 1 over denominator square root of straight I subscript 2 over straight I subscript 1 end root minus 1 end fraction close square brackets squared

rightwards double arrow space open square brackets fraction numerator 5 plus 1 over denominator 5 minus 1 end fraction close square brackets squared space equals space open parentheses 6 over 4 close parentheses squared space equals space 36 over 16 space equals space 9 over 4

Thus space straight I subscript max over straight I subscript min space equals space 9 over 4