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

$$\dfrac{\beta(\mu-1)}{\lambda}\left(\dfrac{t_1}{t_2}\right)$$

B

$$\dfrac{\mu \beta}{\lambda}\dfrac{t_1}{t_2}$$

C

$$\dfrac{\beta(\mu-1)}{\lambda}(t_1 - t_2)$$

D

$$\left(\mu - 1\dfrac{\lambda}{\beta}\right)(t_1 + t_2)$$