When one of the slits of young's experiment is convered with a transparent sheet of thickness 4.8 mm, the central fringe shifts to a position originally occupied by the 30th bright fringe. What should be the thickness of the sheet if the central fringe has to shift to the position occupied by 20th bright fringe?

Options

A. 1.6 mm
B. 3.8 mm
C. 3.2 mm
D. 7.6 mm

Answer

C

Explanation

If with the introduction of a thin transparent medium, the fringe system gets a displacement of m fringes, then we have `(mu-1)t=mlamda`.
For the first case,
`(mu-1)xxt_(1)=m_(1)lamda` . . . (i)
and for the second case,
`(mu-1)xxt_(2)=m_(2)lamda` . . (ii)
Dividing (ii) by (i), we get
`(t_(2))/(t_(1))=(m_(2))/(m_(1))=(20)/(30)`
`thereforet_(2)=(20)/(30)xxt_(1)=(20)/(30)xx4.8mm=3.2mm`.