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)

$\frac{1}{5}\, m/s$

Answer 2

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 $=\frac{1}{5}\,m/s$