Question

In a Young?? double slit experiment with light of wavelength $\lambda$, fringe pattern on the screen has fringe width $\beta$. When two thin transparent glass (refractive index $\mu$) plates of thickness $t_1$ and $t_2$ $(t_1 > t_2)$ are placed in the path of the two beams respectively, the fringe pattern will shift by a distance

• A. $\frac{\beta\left(\mu-1\right)}{\lambda} \left(\frac{t_{1}}{t_{2}}\right)$
• B. $\frac{\mu\beta}{\lambda} \frac{t_{1}}{t_{2}}$
• C. $\frac{\beta\left(\mu-1\right)}{\lambda} \left(t_{1}-t_{2}\right)$
• D. $\left(\mu-1 \right)\frac{\lambda}{\beta} \left(t_{1}+t_{2}\right)$

Answer 1

Answer: (C)

$\frac{\beta\left(\mu-1\right)}{\lambda} \left(t_{1}-t_{2}\right)$

Answer 2

Shift $=\frac{\beta\left(\mu-1\right)}{\lambda}t_{1}- \frac{\beta \left(\mu -1\right)}{\lambda }t_{2}$ $=\frac{\beta \left(\mu -1\right)}{\lambda }\left(t_{1}-t_{2}\right)$