Question

An object is placed at a distance u from a simple microscope of focal length f. The angular magnification obtained depends
(a) on f but not on u
(b) on u but not on f
(c) on f as well as u
(d) neither on f nor on u

Answer 1

(c) on f as well as u

​The angular magnification is the ratio of the angle subtended by the image to the angle subtended by the object on an unaided eye.
In a simple microscope,
$$\begin{gathered} m=\frac{{\displaystyle \raisebox{1ex}{$h$}\!\left/ \!\raisebox{-1ex}{$u$}\right.}}{{\displaystyle \raisebox{1ex}{$h$}\!\left/ \!\raisebox{-1ex}{$D$}\right.}} \\ \mathrm{Here}, \\ u=\mathrm{Object}\mathrm{distance}\mathrm{from}\mathrm{the}\mathrm{lens} \\ D=\mathrm{Image}\mathrm{distance}\mathrm{from}\mathrm{the}\mathrm{lens} \\ h=\mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{object} \end{gathered}$$

In normal adjustment, the object is placed at a distamce equal to ​focal length(f) from the lens and then magnification is given by m = D/f.
For u < f, m = D/f +1.