Question

In Young's double-slit experiment, a mica slab of thickness $t$ and refractive index $\mu$ is introduced in the ray from one of the slits. By how much distance, fringes pattern will be displaced?

• A. $\frac{d}{D}\left(\mu -1\right)t$
• B. $\frac{D}{d}\left(\mu -1\right)t$
• C. $\frac{d}{\left(\mu -1\right)D}$
• D. $\frac{D}{d}\left(\mu -1\right)$

Answer 1

Answer: (B)

The extra path difference due to the insertion of sheet of refractive index $\mu$ and thickness $t$ is,
$\Delta x=(\mu -1)t$
The shift in interference pattern of Young's double slit experiment is,
$y=\frac{D}{d}\Delta x\Rightarrow y=\left(\mu -1\right)t\frac{D}{d}$
Hence, fringes pattern will be displaced by $\frac{D}{d}\left(\mu -1\right)t$ .