Question

How far should an object be placed from the pole of a converging mirror of focal length 20cm to form a real image of the size exactly $\frac{1}{4}$th the size of the object?

Answer 1

Given,
Focal length of the concave mirror (f) = 20 cm
Magnification (m) = -1/4
Using the magnification formula, we get

$$\begin{gathered} m=\frac{-v}{u} \\ \frac{-1}{4}=\frac{-v}{u} \\ v=\frac{u}{4} \\ U\sin gthe\mathrm{mirror}\mathrm{formula},weget \\ \frac{1}{f}=\frac{1}{v}+\frac{1}{u} \\ \frac{1}{-20}=\frac{4}{u}+\frac{1}{u} \\ \frac{-1}{20}=\frac{5}{u} \\ u=-100\mathrm{cm} \\ \mathrm{Thus},\mathrm{the}\mathrm{object}\mathrm{should}\mathrm{be}\mathrm{placed}\mathrm{in}\mathrm{front}\mathrm{of}theco\mathrm{ncave}\mathrm{mirror}\mathrm{at}\mathrm{a}\mathrm{distance}\mathrm{of}100\mathrm{cm}. \end{gathered}$$