In Young's double slit experiment using monochromatic light with a wavelength of
6000Å, the initial fringe width (
β1 ) is 3 mm . We are tasked with determining the new fringe width when the distance between the screen and the slits is increased by
50%, and the distance between the slits is decreased by
10%.
Given:
Wavelength,
λ=6000ÅInitial fringe width,
β1=3mmThe formula for fringe width
(β) in Young's experiment is:
β=where
D is the distance between the screen and the slits, and
d is the distance between the slits. From the given information:
3=Now, recalculating for the changed conditions:
The new distance between the screen and slits,
D′, when increased by
50% :
D′=D+=1.5DThe new distance between the slits,
d′, when decreased by
10% :
d′=d−=0.9dNow, the new fringe width,
β′, is given by:
β′==Substituting Eq. (1) into the equation:
β′=×3 Calculating the above expression:
β′==5mmThus, the new fringe width is 5 mm .
