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) If an object is placed near the eye at a distance less than 25 cm, it appears blurred. The closer object has large angular size than the same object at 25 cm. Due to angular magnification, the eye is able to clearly see the objects placed at the distances lesser than 25 cm because final image is formed at 25 cm.
(b) As the distance of the eye from the lens or object is increased, the angle subtended by the image on the eye decreases, therefore the angular magnification decreases. The effect is almost negligible if the image is formed at very large distance.
(c) Firstly, it is difficult to grind the lenses having very small focal length. If the focal length is decreased, spherical and chromatic aberrations become more pronounced.
(d) Angular magnification of eyepiece is given by `((D)/(f_(e))+1)` (when `f_(e)` is in cm) that increases if `f_(e)` is smaller. Further, magnification of the objective is given by `(v_(o))/(|u_(o)|)=(1)/(|u_(o)|/(f_(o))-1)` which is large when `u_(o)` is slightly smaller than `f_(o)`. A microscope is used for viewing very close objects. So u is small, and so is `f_(o)`. Overall magnification will be multiplication of both the magnifications explained above.
(e) If the eye is positioned too close to the eyepiece, very less light rays refracted from eyepiece will enter in the eye and the field of view of eye will be very small.