In a double-slit experiment, fringes are produced using light of wavelength `4800A^(@)`. One slit is covered by a thin plate of glass of refractive index 1.4 and the other slit by another plate of glass of double thickness and of refractive index 1.7. On doing so, the central bright fringe shifts to a position originally occupied by the fifth bright fringe from the centre. find the thickness of the glass plates.

Options

A. `8 mum`
B. `6 mu m`
C. `4 mu m `
D. `10 mu m`

Answer

A

Explanation

Shift `(Deltax)= (beta)/(lambda)(mu-1)t`
`Deltax_(1)= (beta)/(lambda)(mu_(1)-1)t`
`Deltax_(2)= (beta)/(lambda)(mu_(2)-1)t`
Net shift
`Deltax= Deltax_(2)- Deltax_(1)= (beta)/(lambda)(mu_(2)-mu_(1))t`
Given, `Deltax= 5beta= (beta)/(lambda)[(mu_(2)-mu_(1))t]`
`t= (5lambda)/(mu_(2)-mu_(1))= (5 xx 4800 xx 10^(-10))/(1.7-1.4)= 8 xx 10^(-6)= 8mum`