Question

An object moving at a speed of $ 5\,m/s $ towards a concave mirror of focal length $ f = 1\, m $ is at a distance of $ 9\, m $ . 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 $u=-9\,m$ and $f=-1\,m$
$\frac{1}{(-1)}-\frac{1}{(-9)}=\frac{1}{v}$
$\Rightarrow v=\frac{-9}{8}\,m$
As the object moves at a constant speed of $5 \,m/s$ after $1 \,s$ the new position of image is
$u'=-9m+5m=-4m$
$\therefore \frac{1}{(-1)}-\frac{1}{(-4)}=\frac{1}{v'}$
$\Rightarrow v'=\frac-{4}{3}\,m$
The shift in the position of image in $1s$ is
$v-v'=\frac-{9}{8}+\frac{4}{3} \approx\frac{1}{5}$
$\therefore $ Average speed of image $=\frac{1}{5}\,m/s$