Question

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 $1/4$ is put in front of one of the slits, the central maximum gest shifted by a distance equal to $n$ fringe widths. If the wavelength of light used is $>>,t$ will be :

• A. $\frac{2D\lambda }{a(\mu -1)}$
• B. $\frac{D\lambda }{a(\mu -1)}$
• C. $\frac{2nD\lambda }{a(\mu -1)}$
• D. none of these

Answer 1

Answer: (D)

Path difference at central maxima $\Delta$ x = (μ -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 the question
$t=\frac{n\lambda }{(\mu -1)}$
no option is matching, therefore question
should be awarded bonus.
$\therefore$ Correct Option should be (Bonus)