Question

when is linear and angular magnification equal?

Answer 1

The difference is that of measure; linear magnification is used when projecting an image on a screen and angular when viewing through an eyepiece. Linear Magnification is the ratio of the projected image size (measured with a ruler) over the actual size. Angular magnification is the ratio of the tangent of the angle subtended at the focal point of the eyepiece over the angle subtended at the focal point of the objective.Linear is clear and easy - but you cannot do a linear calcuation for a magnification system with an eyepiece as there is no screen so we use the ratio of the angles (or their tan) instead as this can be observed. If something without magnification covers 1 degree - with 5x Angular magnification it will appear to cover ~5 degrees (at low mag and angles you can almost ignore the tangent).

Answer 2

Yes it can be equal if
ratio of the size of the object and image is equal to the ratio of the angle subtended by object and image