# In a double slit experiment, when a thin film of thickness t having refractive index $\mu$ is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of t is ( $\lambda$ is the wavelenth of the light used) : Option 1) $\frac{\lambda}{2(\mu-1)}$ Option 2) $\frac{2\lambda}{(\mu-1)}$ Option 3) $\frac{\lambda}{(2\mu-1)}$ Option 4) $\frac{\lambda}{(\mu-1)}$

In YDSE

$\triangle X=(\mu-1)\frac{tD}{d}=\beta = \frac{\lambda D}{d}$

$\Rightarrow t=\frac{\lambda}{(\mu-1)}$

Option 1)

$\frac{\lambda}{2(\mu-1)}$

Option 2)

$\frac{2\lambda}{(\mu-1)}$

Option 3)

$\frac{\lambda}{(2\mu-1)}$

Option 4)

$\frac{\lambda}{(\mu-1)}$

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