In Young's slit experiment, if the distance between two slits is halved and the distance between the slits and the screen is doubled then the width of fringe will be.....

Options

A. unchanged
B. halved
C. doubled
D. four times

Answer

D

Explanation

Width of fringe `barx_(1)=(lambda_(1)D_(1))/(2d_(1)) " "...(1)`
Finally widht of ringe `barx_(2)=(lambda_(2)D_(2))/(2d_(2))`
where `d_(2)=(d_(1))/(2),D_(2)=2D_(1) and lambda_(1)=lambda_(2)`
`:. barx_(2)=(lambda_(1)(2D_(1)))/(2((d_(1))/(2)))=(4lambda_(1)D_(1))/(2d_(1))" "...(2)`
Taking ratio of equation (2) and (1)
`(barx_(2))/(x_(1))=(4lambda_(1)D_(1))/(2d_(1))xx(2d_(1))/(lambda_(1)D_(1))`
`:.barx_(2)=4barx_(1)`