Question

In a Young's double slit experiment shown in the figure, a parallel beam of light is incident on the slits from a medium of refractive index ${\mu }_1$.The wavelength of light in this medium is ${\lambda }_1$. A transparent slab of thickness t and refractive index ${\mu }_3$ is put in front of one slit.The refractive index of medium between the screen and the plane of the slits is ${\mu }_2$.Find the phase difference between the light waves at point O (symmetrical, relative to the slits) .

Answer 1

Given,

For Young Double Slit model,

refractive index $=\mu$

Wavelength of light in the medium$={\lambda }_1$

Thickness$=t$

Refractive index$={\mu }_3$ (in transparent slab)

The refractive index of medium between the screen and the plane of the slits $={\mu }_2$

Finding phase difference between the light wave at point O

Path difference of Young double slit model, $=\frac{2\pi }{\lambda }\left(\frac{xd}{D}\right)$

Phase difference $=\frac{2\pi }{\lambda }\times pathdifference=\frac{2\pi }{\lambda }\times \frac{2\pi }{\lambda }\left(\frac{xd}{D}\right)=\frac{4{\pi }^2}{{\lambda }_1^2}\left(\frac{xd}{D}\right)$

Phase difference of Young double slit model is independent of refractive index.