In a Young's double slit experiment with light of wavelength $\lambda ,$ the fringe pattern on the screen has a 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
  $\frac{\beta (\mu - 1)}{\lambda }\left( \frac{t_1}{t_2} \right)$
• B
  $\frac{\mu \beta }{\lambda }\frac{t_1}{t_2}$
• C
  $\frac{\beta (\mu - 1)}{\lambda }(t_1 - t_2)$
• D
  $\frac{(\mu - 1)\lambda }{\beta }(t_1 + t_2)$