Question

23. ) In the Young's arrangement, screen starts moving
towards right with constant speed v. Initial distance
between screen and plane of slits is x. At t = 0,
1st order maxima is lying at point A. After how
much time first order minima lies at point A?
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Answer 1

Given info : In the Young's arrangement, screen starts moving

towards right with constant speed v. Initial distance between screen and plane of slits is x. At t = 0, 1st order maxima is lying at point A.

To find : after how much time first order minima lies at point A.

solution : at t = 0, 1st order Maxima lies at point A.

position of 1st order Maxima, y = λx/d

Where x is distance between slits and screen, d is distance between slits and λ is wavelength of monochromatic light.

Similarly, position of 1st order minima, y' = λx'/2d [ from nth order of minima = (2n-1)λ/2d ]

If 1st order minima concides at point A.

y = y' ⇒λx/d = λx'/2d

⇒x' = 2x

so, shifting of screen = x' - x = 2x - x = x

then time = shifting/speed = x/v

Therefore after x/v time, 1st order minima lies at point A.