Question

An observer finds that 20cm is the least distance from his eye at which he can place a convex mirror of focal length 15cm in order to see his own eye clearly. What is his least distance of distinct vision?

Answer 1

The equation of convex mirror:

$$\frac{1}{d_o}-\frac{1}{d_i}=-\frac{1}{f},\\ \space\\ d_i=\frac{d_of}{d_o+f},\\ \space\\ d_i=\frac{20\cdot15}{20+15}=8.6\text{ cm}.$$

It means that the virtual image produced by the convex mirror is located 8.6 cm behind the surface of the mirror. The least distance of distinct vision, therefore, is

$$d=20+d_i=28.6\text{ cm}.$$