# What is the need for angular magnification

We've been told that angular magnification is defined as the ratio of the angle subtended by the image to the angle subtended by the object. But why would we need a quantity called angular magnification? Won't the simple magnification formula do?

• I'm no specialist here, but I think it would be of no use stating the linear magnification of a telescope, but it means something if it magnifies 20' of sky to 20º after the lenses, for example. – exmachina Feb 26 '17 at 4:25

The angle subtended by an object is called the visual angle and it determines the size of the image formed on the retina.

When you look at the Moon with the naked eye it subtends an angle of about $0.5 ^\circ$.

When looking through a pair of binoculars the angle subtended by the image of the Moon might be $5^\circ$.

The angular magnification is $\dfrac{5}{0.5}=10$

What does that mean? It means that the image of the Moon formed on the retina of the eye when looking through binoculars is ten times bigger than the image formed on the retina when the Moon is looked at directly.
So the Moon appears to be bigger.

In such a context the idea of linear magnification would not be useful because the size of the image of the Moon formed by the binoculars is not ten times the actual size of the Moon.

Linear magnification is only useable in situations where lenses produce real images such as projection onto a screen. Optical instruments with eyepieces such as microscopes produce virtual images whose linear dimensions cannot be measured. Therefore, with these devices, angular magnification is used.