Question

Young's double-slit experiment is conducted in water $\left({\mu }_1\right)$ as shown in figure, and a glass plate of thickness $t$ and refractive index ${\mu }_2$ is placed in the path of $S_2$. Find the magnitude of the phase difference at $O$. [Assume that $\lambda$ is the wavelength of light in air]

• A. $\left|(\frac{{\mu }_2}{{\mu }_1}-1)t\right|\frac{2\pi }{\lambda }$
• B. $|({\mu }_2-{\mu }_1)t|\frac{2\pi }{\lambda }$
• C. $\left|(\frac{{\mu }_1}{{\mu }_2}-1)t\right|\frac{2\pi }{\lambda }$
• D. $|({\mu }_2-1)t|\frac{2\pi }{\lambda }{\mu }_1$

Answer 1

The correct option is B $|({\mu }_2-{\mu }_1)t|\frac{2\pi }{\lambda }$

Wavelength of light in a given medium ${\lambda }_m=\frac{\lambda }{{\mu }_1}$

Path difference due to the introduction of glass slab is given by,

$\Delta x=(\frac{{\mu }_2}{{\mu }_1}-1)t$

Corresponding phase difference is given by,

$\Delta \varphi =\frac{2\pi }{{\lambda }_m}\Delta x$

$\Rightarrow \Delta \varphi =\left(\frac{{\mu }_2-{\mu }_1}{{\mu }_1}\right)\left(t\right)\frac{\left(2\pi \right)}{\lambda }\left({\mu }_1\right)$

$\Rightarrow \Delta \varphi =|({\mu }_2-{\mu }_1)t|\frac{2\pi }{\lambda }$

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