Answer is C.
Optical microscope involves passing visible light transmitted through or reflected from the sample through a single or multiple lenses to allow a magnified view of the sample.
Since my givens are x = .550m [Vsub0] = unknown
[Asubx] = =9.80
[Vsubx]^2 = [Vsub0x]^2 + 2[Asubx] * (X-[Xsub0]
[Vsubx]^2 = [Vsub0x]^2 + 2[Asubx] * (X-[Xsub0])
Vsubx is the final velocity, which at the max height is 0, and Xsub0 is just 0 as that's where it starts so I just plug the rest in
0^2 = [Vsub0x]^2 + 2[-9.80]*(.550)
0 = [Vsub0x]^2 -10.78
10.78 = [Vsub0x]^2
Sqrt(10.78) = 3.28 m/s
The refractive index of water is

. This means that the speed of the light in the water is:

The relationship between frequency f and wavelength

of a wave is given by:

where v is the speed of the wave in the medium. The frequency of the light does not change when it moves from one medium to the other one, so we can compute the ratio between the wavelength of the light in water

to that in air

as

where v is the speed of light in water and c is the speed of light in air. Re-arranging this formula and by using

, we find

which is the wavelength of light in water.