Question

A liquid of refractive index ${\mu }_0$. is filled between slits and screen. Initially the central maxima is at point O on screen, with no slabs in front of slits. Now two slabs of refractive index ${\mu }_1$ and ${\mu }_2$, with thickness $t_1$ and $t_2$ respectively are placed in front of slits as shown, So that the position of central maxima does not change.
Find the ratio of $\frac{t_1}{t_2},$ if ${\mu }_0=1.5,{\mu }_1=1.8$ and ${\mu }_2=2.1$___

Answer 1

The additional path left travelled by ray from a slit due the slab of thickness t and refractive indx $\mu =\frac{\mu }{{\mu }_0}-1)t$
Hence, for the central maxima to remain unchanged the shift due to slabs should be cancelled out
$(\frac{{\mu }_1}{{\mu }_0}-1)t_1=(\frac{{\mu }_2}{{\mu }_0}-1)t_2\therefore \frac{t_2}{t_1}=2$