The figure shows a Young’s double slit experimental setup. It is … - Vidyadip

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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