Question

In a Young’s 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)

Shift $=\frac{\beta \left(\mu -1\right)}{\lambda }{t}_1-\frac{\beta \left(\mu -1\right)}{\lambda }{t}_2$
$=\frac{\beta \left(\mu -1\right)}{\lambda }\left(t_1-t_2\right)$