Question

Interference fringes are produced by a double slit arrangement and a piece of plane parallel glass slab $(\mu =1.5)$ is placed in front of one of the slits. If the fringes are displaced through a distance equal to $30$ fringe widths for light of wavelength $6000\mathring{\text{A}}$, find the thickness of the glass slab.

• A. $0.36\mu \text{m}$
• B. $360\mu \text{m}$
• C. $3.6\mu \text{m}$
• D. $36\mu \text{m}$

Answer 1

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

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

The pattern is shifted through thirty fringes. So, $\Delta x=30\lambda$

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

$(1.5-1)t=30\times 6\times {10}^{-7}$

$t=\frac{18\times {10}^{-6}}{0.5}=3.6\times {10}^{-5}\text{m}=36\mu \text{m}$

Hence, $\left(D\right)$ is the correct answer.