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 (wavelength $\lambda$ ), 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. $2\lambda /3$
• C. $\lambda /3$
• D. $\lambda$

Answer 1

The correct option is A $2\lambda$

$\Delta y=\frac{D(\mu -1)t}{d}$ --(1)
$\Delta y=\frac{\lambda D}{d}----\left(2\right)$ (For having some intensity at central maximum)
$From1and2$
$\frac{\lambda D}{d}=\frac{D(\mu -1)t}{d}$
$\lambda =(1.5-1)t$
$t=\frac{\lambda }{1.5-1}$
$=\frac{\lambda }{0.5}$
$=2\lambda .$