Neco Model Questions Vol1 2017 Physics Question 37

An optical microscope uses an objective lens of focal length \(f_{o}=4\ \text{mm}\) and an eyepiece of focal length \(f_{e}=25\ \text{mm}\). The tube length (distance between the lenses) can be adjusted. When the object is placed just beyond the focal point of the objective, a real intermediate image is formed \(20\ \text{mm}\) from the objective. (i) By how much must the tube length be changed so that the final image is at infinity (relaxed eye)? (ii) What is the angular magnification of the microscope under this condition? (iii) If the microscope is used with light of wavelength \(\lambda=550\ \text{nm}\) and the objective has numerical aperture \(\text{NA}=0.25\), calculate the minimum resolvable distance according to the Rayleigh criterion.