In double slit experiment fringes are obtained using light of wavelength `4800 Å` One slit is covered with a thin glass film of refractive index. `1.4` and another slit is covered by a film of same thickness but refractive index `1.7`. By doing so, the central fringe is shifted to fifth bright fringe in the original pattern. The thickness of glass film is

Options

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

Answer

A

Explanation

When the first glass plate is introduced, the shift in the fringes is given by
`S_(1)=(X)/(lamda)(n_(1)-1)t`
and for the second glass plate of R.I. `(n_(2))`
shift `S_(2)=(X)/(lamda)(n_(1)-1)t` but `n_(2) gt n_(1)`
`therefore S_(2)-S_(1)=(X)/(lamda)[n_(2)-n_(1)]t`
But it is given that `S_(2)-S_(1)=5X`
`therefore 5X=(X)/(lamda)[n_(2)-n_(1)]t`
or `t=(5lamda)/((n_(2)-n_(1)))=(5xx4800xx10^(-10))/((1.7-1.4))`
`=(5xx4.8xx10^(-7))/(0.3)`
`=8xx10^(-6)m=8mum`