Question

The principal axis of an optical device is along $y=-1$, image of a small body placed at ($-30,3$) is formed at a point ($60,-3$). Then the optical device is:-

• A. A convex lens of focal length $20cm$
• B. A concave mirror of focal length $60cm$
• C. A concave lens of focal length $20cm$
• D. A convex mirror of focal length $60cm$

Answer 1

The correct option is A A convex lens of focal length $20cm$

$\begin{array}{c}{h}_0=4cm{h}_i=2cm\\ \text{Magnification}=\frac{h_i}{h_0}=\frac{4}{-2}=-2\\ \text{for lens}\\ \text{magnification}=\frac{v}{u}=-2\end{array}$

$u=-30V=60$

so lens is located at lens formula

$(0,-1)$

$\begin{array}{cc}\frac{1}{f}& =\frac{1}{v}-\frac{1}{u}\\ & =\frac{1}{60}-\frac{1}{-30}\\ \frac{1}{f}& =\frac{1}{60}+\frac{2}{60}\\ & f=\frac{60}{3}=+20cm\end{array}$

So, it is a convex Lens

of focal length $20cm$

option $A$ is Correct