Question

A magnifying lens has a focal length of 100 mm. An object whose size is 16 mm is placed at some distance from the lens so that an image is formed at a distance of 25 cm in front of the lens.
(a) What is the distance between the object and the lens?
(b) Where should the object be placed if the image is to form at infinity?

Answer 1

(a) Given, focal length (f) = 100 mm
Size of object (h) = 16 mm
Image distance (v) = 25 cm = 250 mm

$$\begin{gathered} L\mathrm{ens}\mathrm{formula}\mathrm{is}\mathrm{given}\mathrm{by}: \\ \frac{1}{\mathrm{f}}=\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}} \\ \frac{1}{100}=\frac{1}{250}-\frac{1}{\mathrm{u}} \\ \frac{1}{\mathrm{u}}=\frac{1}{250}-\frac{1}{100} \\ \frac{1}{\mathrm{u}}=\frac{2-5}{500} \\ \frac{1}{\mathrm{u}}=-\frac{3}{500} \\ \mathrm{u}=-166.67\mathrm{mm} \\ \mathrm{u}=-16.66\mathrm{cm} \end{gathered}$$

The object is at a distance of 16.66 cm and in front of the mirror. The image is at a distance of
25 cm and in front of the mirror. Therefore, the distance between the object and the image is 25 cm-16.66 cm = 7.14 cm.

(b) The object should be placed at the focus for the image to be formed at infinity.