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Wave Optics

Question
CBSEENPH12039949
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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

Some More Questions From Wave Optics Chapter

Let us list some of the factors which could possibly influence the speed of wave propagation:
(i) nature of source.
(ii) direction of propagation. 
(iii) motion of source and/or observer.
(iv) wave length.
(v) intensity of the wave.
On which of these factors, if any, does
(a) the speed of light in vacuum,
(b) the speed of light in a medium (say, the glass or water) depend?

For sound waves, the Doppler formula for frequency shift differs slightly between the two situations:
(i) source at rest; observer moving, and
(ii) source moving; observer at rest.
The exact Doppler formulas for the case of light wave in vacuum, are however, strictly identical for these situations. Explain why this should be so. Would you expect the formulas to be strictly identical for the two situations in case of light travelling in a medium?

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