Question

In the ideal double-slit experiment , when a glass-plate (refractive index $1.5$) of thickness $t$ is introduced in the path of one of the interfering beams (wave-length $\lambda )$, the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is

• A. $2\lambda$
• B. $\frac{2\lambda }{3}$
• C. $\frac{\lambda }{3}$
• D. $\lambda$

Answer 1

The correct option is A $2\lambda$

The shift due to glass plate is given by $(\mu -1)t$
For the case given, $(\mu -1)t=n\lambda$
For the minimum thickness $n=1$
$(\mu -1)t=\lambda$
$t=\frac{\lambda }{(\mu -1)}$
$t=\frac{\lambda }{(1.5-1)}$
$t=2\lambda$