When you spread oil

$($noil $=1\mathrm{.}50)$

on water

$($nwater $=1\mathrm{.}33)$

and have white light incident from above, you might observe different reflected colors that depend on the thickness of the oil on the water at each point. Consider the wavelength of red light

$(745\mathrm{.}0$ nm$)$

and the wavelength of violet light

$(417\mathrm{.}0$ nm$),$

covering the visible spectrum. What is the minimum possible thickness of the oil that would give rise to the following.

$($a$)$ seeing the red light

$(745\mathrm{.}0$ nm$)$

reflected

m

$($b$)$ seeing the violet light

$(417\mathrm{.}0$ nm$)$

reflected