Q

I need help with - Optics - JEE Main-2

The figure shows a Young's double slit experimental setup. It is observed that when a thin transparent sheet of thickness $t$ and refractive index $\mu$ is put in front of one of the slits , the central maximum gets shifted by a distance equal to $n$ fringewidths. If the wavelength of lightused is $\lambda ,t$ will be :

• Option 1)

$\frac{2nD\lambda }{a\left ( \mu -1 \right )}$

• Option 2)

$\frac{nD\lambda }{a\left ( \mu -1 \right )}$

• Option 3)

$\frac{D\lambda }{a\left ( \mu -1 \right )}$

• Option 4)

$\frac{2D\lambda }{a\left ( \mu -1 \right )}$

Views

If sheet is placed infront of one slit ,

displacement of fring    $=\frac{D}{d}\left ( \mu-1 \right )t$               here $d=a$

given,              $\frac{n\lambda D}{d}=\frac{D}{d}\left ( \mu-1 \right )t$

$t=\frac{n\lambda }{\mu-1}$

Option 1)

$\frac{2nD\lambda }{a\left ( \mu -1 \right )}$

Option 2)

$\frac{nD\lambda }{a\left ( \mu -1 \right )}$

Option 3)

$\frac{D\lambda }{a\left ( \mu -1 \right )}$

Option 4)

$\frac{2D\lambda }{a\left ( \mu -1 \right )}$

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