$1.$ A non$-$reflective coating that has a thickness of $162$ nm $($n $=1\mathrm{.}45)$ is deposited on top of a substrate of glass $($n $=1\mathrm{.}50).$ What wavelength of visible light is most strongly reflected if it is illuminated perpendicular to its surface?

$2.$ You are using a hydrogen discharge tube and high quality red and blue light filters as the light source for a Michelson interferometer. The hydrogen discharge tube provides light of several different wavelengths $($colors$)$ in the visible range. The red light in the hydrogen spectrum has a wavelength of $656\mathrm{.}3$ nm and the blue light has a wavelength of $434\mathrm{.}0$ nm$.$ When using the discharge tube and the red filter as the light source, you view a bright red spot in the viewing area of the interferometer. You now move the movable mirror away from the beam splitter and observe $142$ bright spots. You replace the red filter with the blue filter and observe a bright blue spot in the interferometer. You now move the movable mirror towards the beam splitter and observe $118$ bright spots. Determine the final displacement $($include sign$)$ of the moveable mirror. $($Assume the positive direction is away from the beam splitter.$)$