In figure S is a monochromatic source of light emitting light of wavelength of wavelength `lambda` (in air). Light on slits `S_(1)` from S and then reaches in the slit `S_(2)` and `S_(3)` through a medium of refractive index `mu_(1)`. Light from slit `S_(2)` and `S_(3)` reaches the screen through a medium of refractive index `mu_(3)`. A thin transparent film of refractive index `mu_(2)` and thickness t is used placed in front of `S_(2)`. Point P is symmetrical w.r.t. `S_(2)` and `S_(3)`. Using the values `d = 1 mm, D = 1 m, mu_(1) = 4//3`,
`mu_(2) = 3//2, mu_(3) = 9//5`, and `t = (4)/(9) xx 10^(-5) m`,
a. find distance of central maxima from P,
b. If the film in front of `S_(2)` is removed, then by what distance and in which direction will be central maxima shift ?
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