Question

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

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

Answer 1

The correct option is C $1.16\times {10}^{-3}\text{m/s},$ towards the lens

Given:
Focal length, $f=+0.3\text{m}$
Object distance, $u=-20\text{m}$
velocity of object, $V_o=-5\text{m/s}$

(Considering velocity is +ve towards right direction)

Using relation between speed of image & speed of object:

$V_i={\left(\frac{f}{f+u}\right)}^2{V}_o$

$V_i={\left(\frac{0.3}{0.3-20}\right)}^2{V}_0={\left(\frac{0.3}{-19.7}\right)}^2\times (-5)$

$V_i=-1.16\times {10}^{-3}\text{m/s}$

$\therefore V_i=1.16\times {10}^{-3}\text{m/s}$, towards lens.

Hence, $\left(c\right)$ option is correct.

Why this question? To understand the relation between speed of object & speed of an image with sign convention.