A concave mirror of focal length \(20 \mathrm{~cm}\) forms image \(1 / 2\) the size of the object. determine the object distance ____________
A. \(20 \mathrm{~cm}\)
B. \(60 \mathrm{~cm}\)
C. 100 cm
D. 80 cm
Correct Answer: B
Explanation
given: \(\mathrm{f}=20 \mathrm{~cm}\)
\(\mathrm{m}=1 / 2=\frac{\mathrm{v}}{\mathrm{u}}, u=2 \mathrm{v}\) or \(\mathrm{v}=\frac{\mathrm{u}}{2}\)
to determine \(u\) ?
using
\(\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{u}}+\frac{1}{\mathrm{v}}\)
\(\frac{1}{20}=\frac{1}{\mathrm{u}}+\frac{1}{\mathrm{u} / 2}\)
\(\frac{1}{20}=\frac{1}{\mathrm{u}}+\frac{2}{\mathrm{u}}\)
\(\frac{1}{20}=\frac{1+2}{\mathrm{u}}\)
\(\frac{1}{20}=\frac{3}{\mathrm{u}}\)
\(\mathrm{u}=20 \times 3=60 \mathrm{~cm}\)