A Young's double slit apparatus is immersed in a liquid of refractive index `mu_(1).` The slit plame touches the liquid surface. A parallel beam of monochromatic light of wavelength `lambda` (in air) is incident normally on the slits.
a. Find the fringe width.
b. If one of the slits (say `S_(2)`) is covered by a transparent slab of refrative index `mu_(2)` and thickless t as shown, find the new position of central maxima.
c. Now, the other slit, `S_(1)` is also covered by a slab of same thickness and refractive index `mu_(3)` as shown in Fig. 2.49 due to which the central maxima recovers it positon, find the value of `mu_(3)`
Find the ratio of intensities at O in the three conditions (a), (b), and (c).

Answer

`[(a)(lambdaD)/(mu_(1)d);(b) ((mu_(2)-1)tD)/(d);(c ) mu_(1)mu_(2); (d) 1 : cos ^(2){(pi(mu_(2)-1)t)/(lambda)}:1]`