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. (a) `8mum`
B. (b) `6mum`
C. (c) `4mum`
D. (d) `10mum`

Answer

A

Explanation

Shift `Deltax=beta/lambda(mu-1)t`

Shift due to one plate `Deltax_1=beta/lambda(mu_1-1)`
Shift due to another path `Deltax_2=beta/lambda(mu_2-1)t`
Net shift `Deltax=Deltax_2-Deltax_1=beta/lambda(mu_2-mu_1)t` ...(i)
Also it is given that `x=5beta` ...(ii)
Hence `5beta=beta/lambda(mu_1-mu_2)t`
`impliest=(5lambda)/((mu_1-mu_2))=(5xx4800xx10^(-10))/((1.7-1.4))`