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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 )}

 
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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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