Question

Assuming a wave length of 0.5 um, calculate the optimum resolution of your microscope for each of the objectives –4x, 10x, 40x, and 100x, using the NA value marked on each objective.

Answer 1

Resolution is calculated by Abbe's formula

d= (wavelength / 2) * NA

NA= n * sin , where n is the refractive index, the refractive index of 100x objective is 1.52 as the medium used is oil (it is usually an oil immersion objective) for others it's 1. Maximum angle is 144 degrees. Hence NA for 100x shall be 1.45 and for others 0.95. I am assuming the angle to be 144 degrees since you haven't provided the same or NA values.

for 4x, 10x, 40x the resolution is : (0.5 micrometer / 2) * 0.95 = 0.2375 micrometer

for 100x: (0.5 micrometer / 2) * 1.45 = 0.2375 micrometer= 0.3625 micrometers