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  4. A luminous point object is moving along the principal axis of a concave mirror of focal length 12 cm towards it. When its distance from mirror is 20 cm its velocity is 4 cm / s. The velocity of the image in cm / s at that instant is :

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Q. A luminous point object is moving along the principal axis of a concave mirror of focal length $12 cm$ towards it. When its distance from mirror is $20 cm$ its velocity is $4 cm / s$. The velocity of the image in $cm / s$ at that instant is :

Ray Optics and Optical Instruments

Solution:

Using mirror formula
$v=+30 cm $ as $f =12\,\,\,\, u =-20$
Now, $\frac{d u}{d t}\left(\frac{-1}{u^{2}}\right)=\frac{1}{v^{2}}\left(\frac{d v}{d t}\right)$
$\frac{d u}{d t}=-4$ (towards mirror so -ve)
$\therefore \frac{4}{20^{2}}=\frac{1}{30^{2}} \times \frac{d v}{d t}$
So $\frac{d v}{d t}=9 cm / s$
+ve so away from the mirror.