What is effect on the interference fringes in a Young's double slit experiment due to each of the following operations :
(a) the screen is moved away from the plane of the slits,
(b) the monochromatic source is replaced by another monochromatic source of shorter wavelength,
(c ) the separation between the two slits is increased,
(d) the source slit is moved closer to the double slit plane,
(e) the width of the source slit is increased.
(f) the width of two slits are increased,
(g) the monochromatic source is replaced by a source of white light ?
(In each operation, take all parameters, other than the one specified, to remain unchanged) NCERT Solved Example

Explanation

(a) When screen is moved away, `D` increases.
As `beta = (lambda D)/(d)`
therefore width of the fringes increases. However, angular separation `(lambda//d)` remains the same.
(b) Here, `lambda` decreases
`:.` `beta` decreases i.e., fringe width decreases.
( c) When separation between slits is increased, `d` increases. Therefore fringe width `beta` decreases.
(d) If `s` is size of the source and `S` is distant of source from the plane of the two slits, then for interference fringes to seen, the condition is
`(s)/(S) lt (lambda)/(D)`
As source slit is brought closer to double slit plane, `S` decreases, teh interference pattern gets less and less sharp. When the source is too close, the fringe separation remains fixed.
(e) As width of source slit is increased, the interference pattern gets less and less sharp. When the source slit is so wide that conditon
`(s)/(S) lt (lambda)/(D)` is violated, the interference pattern disappears.
(f) When the widths of the two slits are increased, the fringes become brigther. However, width of each slit should be considerably smaller than the separation between the slits. When the slits becomes so wide that this condition is not satisfied, the interference pattern disappears.
(g) When a source of white light is used, central fringe is white. As blue has lowest value of `lambda`, the fringe closest on both sides of central white fringe is blue and the farthest fringe is red. After a few coloured fringes, the pattern disappears.