a) The anlge subtended at the eye by an object is equal to the angle subtended at the eye by the virtual image produced by a magnifying glass. In what sense then does a magnifying glass provide angular magnifications?
b) in viewing through a magnifying glass, one usually positions one's eyes very close to the lens. Does angular magnification change if the eye is moved back?
c) magnifying power of a simple microscopes is inversely proportional to the focal length of the lens. What then stops us from using a convex lens of smaller and smaller focal length and achieving greater and greater magnifying power?
d) Why must both the objective and the eyepiece of a compound microscope have short focal lengths?
e) When viewing through a compound microscope, our eyes should be positioned not on the eyepiece but a short distance away from it fot best veiwing. Why? How much should be that short distance between the eye and eyepiece?

Explanation

(a) It is true that angular size of image is equal to angular size of the object.
By using magnifying glass, we keep the object far more closer to the eye than at `25 cm`, its normal position without use of glass. The closer object has larger angular size than the same object at `25 cm`. it is in this sense that angular magnification is achieved.
(b) Yes, the angular magnification changes, if the eye is moved back. This is becasue angle subtended at the eye would be slightly less than the angle subtended at the lens. The effect is negligible when imafe is at much larger distance.
( c) Theoretically, it is true. However, when we decrease focal length, aberrations both spherical and chromatic become more pronounced. Further, it is difficult to grind lenses of very small focal lengths.
(d) Angular magnification of eye piece is `(1 + (d)/(f_(e)))`. This increases as `f_(e)` decreases.
Further, magnification of objective lens is `(v)/(u)`. As object lies close to focus of objective lens `u = f_(0)`. To increases this magnification `(v//f_(0)), f_(0)` should be smaller.
(e) The image of objective lens in eye piece is called 'eye ring'. All the rays from the object refracted by the objective go through the eye ring. Therefore, ideal position for our eyes for viewing is this eye ring only.
When eye is too close to the eye piece, field of view reduces and eyes do not collect much of the light. The precise location of the eye ring would depend upon the separation between the objective and eye piece, and aslo on focal length of the eye piece, field of view reduece and eyes fo not collect much of the light. The precise location of the eye ring would depend upon the separation between the objective and eye piece, and also on focal length of the piece.