Question

A convex lens of focal length $30cm$ forms an image of height $2cm$ for an object situated at infinity. If a concave lens of focal length $20cm$ is placed coaxially at a distance of $26cm$ in front of convex lens the size image would be

• A. $2.5cm$
• B. $5.0$
• C. $1.25$
• D. None

Answer 1

Answer: (C)

$\begin{array}{c}{f}_1=30cm\\ f_2=(-20cm)\text{Because concave}\end{array}$

$\begin{array}{c}{u}_2=4cm\\ u_1=\infty \\ \text{Using lens formula}\end{array}$

$\begin{array}{c}\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\\ \frac{1}{v}-\frac{1}{4}=-\frac{1}{20}\end{array}$

$\begin{array}{cc}v& =5cm\\ \text{Magnification}& \\ m& =\frac{v}{u}\\ & =\frac{5}{4}\\ & =1.25cm\end{array}$