MCQ
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 $n$ fringe widths. If the wavelength of light used is $\lambda ,\,t$ will be
  • A
    $\frac{{2nD\lambda }}{{a\left( {\mu  - 1} \right)}}$
  • B
    $\frac{{nD\lambda }}{{a\left( {\mu  - 1} \right)}}$
  • C
    $\frac{{2D\lambda }}{{a\left( {\mu  - 1} \right)}}$
  • $\frac{{n\lambda }}{{\left( {\mu  - 1} \right)}}$

Answer

Correct option: D.
$\frac{{n\lambda }}{{\left( {\mu  - 1} \right)}}$
d
Path difference at central maxima $\Delta x=(\mu-1)\, t,$ whole pattern will shift by same amount which will be given by

$(\mu-1) \,t \frac{D}{d}=n \frac{\lambda D}{d},$ according to eh question $t=\frac{n \lambda}{(\mu-1)}$

No option is matching, therefore question should be award bonus.

$\therefore $ Correct option should be (Bonus)

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