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Q.

In a double slit experiment suppose that light emerging from the slits is intense enough to reach far off distances on the screen. Usually, the fringe width is expressed as  λDd, where the symbols have their usual meanings; but this is true only if  y<<D, where y is the distance on the screen from the central bright fringe to the point of observation. If the fringe width is  pλD/d  at an angular position, θ=π3 relative to the central axis. Then find p. (Note that here y is comparable to  D).

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answer is 8.

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Detailed Solution

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d sinφ = nλ   …………. (1)
 d sin(φ+dφ) = (n+1)λ ……….. (2)
(2) –(1)  gives   
  d cos φ . dφ = λ   …….. (3)     
since Tan φ = y/ D
and differentiating  here dφ = β/ 4D and φ = π/3 
on substitutions in 3 we get  β= 8λD/d

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