$4.($a$)$ In a Michelson Interferometer, illmminated with a laser souree of $600$ nm $,$ one of the mirror is moving with a velocity $\backslash (5\backslash$mathrm$\{$~mm$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The interference signal is observed at the detection arm using a photodiode and an oscilloscope. $($i$)$ Calculate the frequency of the observed time$-$varying signal. $($ii$)$ How many number of bright fringes are observed during the motion of the mirror by $300$ micrometer?

$($b$)$ A laser is illuminating two slits separated by $0\mathrm{.}01$ mm $.$ It was observed that the third bright fringe is formed at an angle $10\mathrm{.}95$ degree. Calculate the wavelength of the light source.

$($c$)$ What is the maximum possible distance over which a millimeter scale marks cist he visible through naked cyes, Assume the pupil $($aperture$)$ diameter is $3$ mm $.[3]$