Question

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

• A. $1.8\times {10}^{-3}\text{cm}$
• B. $5.4\times {10}^{-3}\text{cm}$
• C. $3.6\times {10}^{-3}\text{cm}$
• D. $7.2\times {10}^{-3}\text{cm}$

Answer 1

The correct option is C $3.6\times {10}^{-3}\text{cm}$

The formula for fringe shift is given by,
$\Delta y=\frac{\beta }{\lambda }(\mu -1)t$

Here,
$\Delta y=30\beta$

$\Rightarrow (\mu -1)t=30\lambda$

$\therefore$ $t=\frac{30\lambda }{\mu -1}=\frac{30\times 6\times {10}^{-5}\times {10}^{-2}}{1.5-1}$

$=3.6\times {10}^{-3}\times {10}^{-2}\text{m}=3.6\times {10}^{-3}\text{cm}$

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