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In Young's double-slit experiment, a poi...

In Young's double-slit experiment, a point source is placed on a solid slab of refractive index `6//5` at a distance of 2 mm from two slits spaced 3 mm apart as shown and at equal distance from both the slits. The screen is at a distance of 1 m from the slits. Wavelength of light used is 500 nm.
a. Find the position of the central maximum.
b. Find the order of the fringe formed at O.
c. A film of refractive index 1.8 is to be placed in front of `S_(1)` so that central maxima is formed where 200th maxima was formed. Find the thickness of film.

Text Solution

Verified by Experts

The correct Answer is:
a. `(-1)/(6)` m (below 0)
b. 750
c. 1.25 mm
At P any point on the screen, optical path diffenence between `SS_(2) P` and `SS_(1) P` is zero
`(SS_(2) - SS_(1) P)_("optical") = 0`
`y = - SS_(2) (mu - 1) (D)/(d) = - 2.5 ((1)/(5)) xx (10^(3))/(3) = (-1)/(6) m` (below 0)
b. Order of fringe at O is
`(lambda)/(lambda D//d) = (1 xx 3 xx 10^(-3))/(6 xx 500 xx 1 xx 10^(-9)) = 750`
c. `t (mu' - 1) = 200 lambda implies t = 1.25 mm`.
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