A convex lens of focal length \(10.0 cm\) is used to form a real image which is half the size of the object. How far from the object is the image?
Explanation
\(f=10.0 cm\), magnification \(m=1 / 2\)
Required image; distance \(v=\) ?
\(m=v / u\),
\(v=\frac{1}{2} \times u\)
using the lens formula
\(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\)
\(\frac{1}{10}=\frac{1}{u}+\frac{1}{u / 2}=\frac{1}{u}+\frac{2}{u}\);
\(\frac{1}{10}=\frac{3}{u}, u=30 cm\)
\(v=\frac{u}{2}=15 cm\)
the image is \(45 cm\)
\((15 cm +30 cm )\) from the object
