A microscope has a numerical aperture sin a 0.12, where a is the aperture angle subtended

Question:

A microscope has a numerical aperture sin a – 0.12, where a is the aperture angle subtended by the entrance pupil of tile microscope. Assuming the diameter of an eye’s s pupil to be equal to do = 4.0 ram, determine the microscope magnification at which
(a) The diameter of the beam of light coming from the microscope is equal to the diameter of tile eye's pupil;
(b) The illuminance of the image on the retina is independent of magnification (consider the case when the beam of light passing through the system "microscope-eye" is bounded by the mounting of the objective).