Physics - Wave Optics Question with Solution | TestHub

The lateral displacement (shift) of the fringes when a thin transparent plate is introduced in the path of one of the interfering beams is given by the formula:

$\Delta x=\frac{D}{d}(\mu -1)t$

Given values are:
Distance between screen and slits, $D=1\text{ m}$
Distance between the slits, $d=2\text{ mm}=2\times 10^{-3}\text{ m}$
Refractive index of the glass plate, $\mu =1.5$
Thickness of the glass plate, $t=0.04\text{ mm}=4\times 10^{-5}\text{ m}$

Substituting the given values into the formula:

$\Delta x=\frac{1}{2\times 10^{-3}}(1.5-1)\times 4\times 10^{-5}$

$\Delta x=\frac{1}{2\times 10^{-3}}\times 0.5\times 4\times 10^{-5}$

$\Delta x=\frac{2\times 10^{-5}}{2\times 10^{-3}}$

$\Delta x=10^{-2}\text{ m}$

$\Delta x=1\text{ cm}$

Answer: 1 cm