Question

A point object moving on principle axis of convex lens of focal length 20 cm is at distance of 60 cm from it at any instant. If the speed of object is 3 m/s, then speed of image is

• A. $3m/s$
• B. $\frac{5}{4}m/s$
• C. $\frac{2}{3}m/s$
• D. $\frac{3}{4}m/s$

Answer 1

The correct option is D $\frac{3}{4}m/s$

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\Rightarrow f^{-1}=v^{-1}-u^{-1}$

$0=-v^{-2}\left(\frac{dv}{dt}\right)+u^{-2}\left(\frac{du}{dt}\right)\Rightarrow \frac{v_I}{u^2}=\frac{v_0}{u^2}$

$v_I=\frac{v^2}{u^2}{v}_0\Rightarrow \frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$\frac{1}{20}=\frac{1}{v}-\frac{1}{-60}\Rightarrow \frac{1}{v}=\frac{1}{20}-\frac{1}{60}\Rightarrow v=30cm$

$v_I={\left(\frac{30}{60}\right)}^2\times 3m/s=\frac{3}{4}m/s$