Angular and Linear Magnification

## Question:

Q1: Why is angular magnification M not always the same as the linear magnification m? Is it because we have made an assumption that when M = m, then the vision angle must be very small, i.e. alpha = tangent alpha?

Q2: In a compound microscope(having 2 convex lenses), why it is not good to use lens with long focal length? I find an equation that magnification M = (D/f +1), where D = least distance of distinct vision & f = focal length. So it seems that if f is large, then the magnification will be small, so short focal length lenses are preferred. But how can I prove the equation mathematically?

Q1. Linear magnification is the ratio of the size of object and image. Angular magnification is the ratio of the angle subtended by object and image. Subtended angles are related to the linear size by non-linear trigonometric functions and depend on the distance from image to eye. The small angle approximation is used to simplify the ratio of subtended angles to m=1+D/f.

Q2. The overall magnification of the microscope is the product of the linear magnification of the objective lens and the angular magnification of the eyepiece with the first image at the focal length.