Question

A mica slit of thickness $t$ and refractive index $\mu$ is introduced in the ray from the first source $S_1$. By how much distance the fringe pattern will be displaced ?

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

Answer 1

Answer: (B)

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

Path difference introduced due to insertion of mica slit = $t(\mu -1)$

Distance of fringe from mean position is given as

$\beta =\frac{Dy}{d}$

Thus $\Delta \beta =\frac{D\Delta y}{d}$

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

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