Question

Interference fringes are produced by a double slit arrangement and a plane parallel glass of refractive index $1.5$ is placed in front of one of the interfering beam. If the fringes are displaced through $30$ fringe width for light of wavelength $6\times {10}^{-5}\text{cm}$, then the thickness of the plate will be:

• A. $4\mu \text{m}$
• B. $48\mu \text{m}$
• C. $36\mu \text{m}$
• D. $2.4\mu \text{m}$

Answer 1

The correct option is C $36\mu \text{m}$

Path difference due to glass slab,
$\Delta x=(\mu -1)t$

Shift in fringe pattern produced due to glass slab is,
$\Delta y=\frac{(\mu -1)tD}{d}=\frac{(\mu -1)t\beta }{\lambda }$

$(\because \beta =\frac{\lambda D}{d})$

According to question, fringe pattern gets shifted by $30$ fringe width.

$\Rightarrow \Delta y=30\beta$

$\Rightarrow \frac{(\mu -1)t\beta }{\lambda }=30\beta$

$\Rightarrow t=\frac{30\lambda }{\mu -1}$

$\Rightarrow t=\frac{30\times 6\times {10}^{-7}}{1.5-1}$

$\Rightarrow t=36\times {10}^{-6}\text{m}=36\mu \text{m}$

Hence, option $\left(C\right)$ is correct.