Question

An object moving at a speed of $5m/s$ towards a concave mirror of focal length $f=1m$ is at a distance of $9m$ . The average speed of the image is

• A. $\frac{1}{5}m/s$
• B. $\frac{1}{10}m/s$
• C. $\frac{5}{9}m/s$
• D. $\frac{4}{9}m/s$

Answer 1

Answer: (A)

According to mirror formula
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
Here $u=-9m$ and $f=-1m$
$\frac{1}{(-1)}-\frac{1}{(-9)}=\frac{1}{v}$
$\Rightarrow v=\frac{-9}{8}m$
As the object moves at a constant speed of $5m/s$ after $1s$ the new position of image is
$u^{\prime }=-9m+5m=-4m$
$\therefore \frac{1}{(-1)}-\frac{1}{(-4)}=\frac{1}{v^{\prime }}$
$\Rightarrow v^{\prime }=\frac{-}{4}3m$
The shift in the position of image in $1s$ is
$v-v^{\prime }=\frac{-}{9}8+\frac{4}{3}\approx \frac{1}{5}$
$\therefore$ Average speed of image $=\frac{1}{5}m/s$