Question

A point source of light is moving at a rate of 2 cm-s${}^{-1}$ towards a thin convex lens of focal length 10 cm along its optical axis. When the source is 15 cm away from the lens the image is moving at

• A. 4 cm-s${}^{-1}$ towards the lens
• B. 8 cm-s${}^{-1}$ towards the lens
• C. 4 cm-s${}^{-1}$ away from the lens
• D. 8 cm-s${}^{-1}$ away from the lens

Answer 1

The correct option is D

8 cm-s${}^{-1}$ away from the lens

$\frac{dv}{dt}=\frac{-v^2}{u^2}\frac{du}{dt}$

$\&\frac{1}{v}=\frac{1}{F}+\frac{1}{u}$

$\frac{1}{V}=\frac{1}{10}+\frac{1}{-15}$

$\frac{1}{v}=\frac{3-2}{30}$

v =30 cm

$\frac{dv}{dt}={\left(\frac{1}{F}\right)}^2.2$

=8 cm/s away from lens