Solution

(a) Though the image size is bigger than the object, the angular size of the image is equal to the angular size of the object. A magnifying glass helps one see the objects placed closer than the least distance of distinct vision (i.e., 25cm). A closer object causes a larger angular size. A magnifying glass provides angular magnification. Without magnification, the object cannot be placed closer to the eye. With magnification, the object can be placed much closer to the eye.

(b) Yes, the angular magnification changes. When the distance between the eye and a magnifying glass is increased, the angular magnification decreases a little. This is because the angle subtended at the eye is slightly less than the angle subtended at the lens. Image distance does not have any effect on angular magnification.

(c) The focal length of a convex lens cannot be decreased by a greater amount. This is because making lenses having very small focal lengths is not easy. Spherical and chromatic aberrations are produced by a convex lens having a very small focal length.

(d) Angular magnification of eye-piece is $$[(25/f_e) + 1]$$ ($$f_e$$ in cm) which increases if $$f_e$$ is smaller. Further, magnification of the objective
is given by $$\displaystyle \frac{V_o}{\left|u_o\right|} = \frac{1}{\left(\left|u_o\right| / f_o\right)-1}$$
which is large when $$\left|u_o\right|$$ is slightly greater than $$f_o$$. The microscope is used for viewing very close object. So $$\left|u_o\right|$$ is small, and so is $$f_o$$.

(e) When we place our eyes too close to the eyepiece of a compound microscope, we are unable to collect much refracted light. As a result, the field of view decreases substantially. Hence, the clarity of the image gets blurred.
The best position of the eye for viewing through a compound microscope is at the eye-ring attached to the eyepiece. The precise location of the eye depends on the separation between the objective lens and the eyepiece.