Question 204: Wave Optics

Question

As shown in the figure, in Young's double slit experiment, a thin plate of thickness $$t=10 \mu \mathrm{m}$$ and refractive index $$\mu=1.2$$ is inserted infront of slit $$S_{1}$$. The experiment is conducted in air $$(\mu=1)$$ and uses a monochromatic light of wavelength $$\lambda=500 \mathrm{~nm}$$. Due to the insertion of the plate, central maxima is shifted by a distance of $$x \beta_{0} . \beta_{0}$$ is the fringe-width befor the insertion of the plate. The value of the $$x$$ is _____________.

Accepted Answer

Given $\mathrm{t}=10 	imes 10^{-6} \mathrm{~m}$
$$
\begin{aligned}
& \mu=1.2 \\
& \lambda=500 	imes 10^{-9} \mathrm{~m}
\end{aligned}
$$
When the glass slab inserted infront of one slit then the shift of central fringe is obtained by
$

\mathrm{t}=\frac{\mathrm{n} \lambda}{(\mu-1)} $
$
\Rightarrow \quad 10 	imes 10^{-6}=\frac{\mathrm{n} 	imes 500 	imes 10^{-9}}{(1.2-1)} $
$$ \Rightarrow $$ $
10 	imes 10^{-6}=\frac{\mathrm{n} 	imes 500 	imes 10^{-9}}{0.2} $
$$ \Rightarrow $$ $
\mathrm{n}=4

$

Wave Optics

Integer / Numeric Answer Type