Question

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

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

also $\frac{1}{v}=\frac{1}{10}+\frac{1}{-15}$, v=30

so $\frac{dv}{dt}=\frac{-{30}^2}{{15}^2}\times 2$

that is 8 cm/s away from the lens.