Question

An object is at a distacen of $20m$ from a convex lens of focal length $0.3m$. The lens forms an image of the object. If the object moves away from the lens at a speed of $5m/s$, the speed and direction of the image will be :

• A. $0.92\times 10^{-3}m/s$ away from the lens
• B. $2.26\times 10^{-3}m/s$ away from the lens
• C. $1.16\times 10^{-3}m/s$ towards the lens
• D. $3.22\times 10^{-3}m/s$ towards the lens

Answer 1

Answer: (C)

From lens equation
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}-\frac{1}{\left(-20\right)}=\frac{1}{\left(.3\right)}=\frac{10}{3}$
$\frac{1}{v}=\frac{10}{3}-\frac{1}{20}$
$\frac{1}{v}=\frac{197}{60};v=\frac{60}{197}$
$m=\left(\frac{v}{u}\right)=\frac{\left(\frac{60}{197}\right)}{20}$
velocity of image wrt. to lens is given by vI/L = m2vO/L
direction of velocity of image is same as that of object
vO/L = 5 m/s
$v_{I/L}={\left(\frac{60\times 1}{197\times 20}\right)}^2\left(5\right)$
= $1.16\times 10^{-3}m/s$ towards the lens