$(10$pt$)$ Consider the Michelson's interferometer.

$($a$)$ Briefly draw and explain about the Michelson's interferometer.

$($b$)$ A thin film with index of refraction $n=1\mathrm{.}6$ is inserted on one of the arms. The film is inserted perpendicularly to the path of the beam. If the wavelength of the beam is $450$ nm and the pattern is shifted for $914$ fringes, evaluate the thickness of the film.

$($c$)$ How much is the adjustment of the distance between the beam splitter and the mirror on one arm to make the same number of shifts on the $($b$)?$