An object is \(5 cm\) away from the pole of a convex lens whose radius of curvature is \(30 cm\). What is the nature of the object's image?
Explanation
Using Lens formula,
\begin{aligned}
\frac{1}{f} &=\frac{1}{u}+\frac{1}{v} ; r=30 cm \\
f &=\frac{30}{2}=15 cm , u=5 cm \\
\frac{1}{15} &=\frac{1}{v}+\frac{1}{5} \\
\frac{1}{v} &=\frac{1}{15}-\frac{1}{5} \\
\frac{1}{v} &=\frac{1-3}{15}=\frac{-2}{15} \\
v &=-7.5 cm \\
m &=\left|\frac{v}{u}\right|=\left|\frac{-7.5}{5}\right|=1.5
\end{aligned}
thus, image is virtual and magnified (since \(m>1\) )
