Question

object velocity 2cm/s towards concave mirror of focal length 20cm. the object is at 10 cm what is velocity of image​

Answer 1

mirror formula of a constant focal length f is given as ..

1/v + 1/u = 1/f

differentiating both sides with respect to time,

or, -1/v² dv/dt - 1/u² du/dt = 0

or, 1/v² dv/dt = -1/u² du/dt

or, dv/dt = -(v/u)² du/dt

or, $V_{im}=-\left(\frac{v}{u}\right)^2V_{om}$

here, $V_{im}$ is velocity of image with respect to mirror, $V_{om}$ is velocity of object with respect to mirror.

given, f = -20cm, u = -10cm, $V_{om}$ = 2cm/s

so, 1/v + 1/-10 = 1/-20

or, 1/v = -1/20 + 1/10 = 1/20

or, v = +20cm

now $V_{im}$ = -(20/-10)² × 2cm/s = -8cm/s

hence, velocity of image is 8cm/s towards mirror from other side of mirror.