Question

An object Is 24 CM away from a concave mirror and it's image is 16 CM from the mirror find the focal length and radius of curvature of the mirror and the magnification of the image

Answer 1

See, here we are given :

1. u = -24 cm and

2. v = +/- 16 cm (since we are not provided if image is real or virtual)

Now we have two cases,

Case 1: v = + 16 cm

So by Mirror formula ie 1/f = 1/v + 1/u

$1/f = 1/16 + 1/(-24)\\1/f = 1/16 - 1/24\\1/f = (3-2)/48\\f = + 48 cm$

But as concave mirror has the property of focal length -ve  so answer can't be +48 cm

Case 2: v = -16 cm

So by Mirror formula ie 1/f = 1/v + 1/u

$1/f = 1/(-16) + 1/(-24)\\1/f = -1/16 - 1/24\\1/f = (-3-2)/48\\f = -48/5 cm$

So f = -9.6 cm

Also r = 2f

So r = -19.2 cm

*Here we are having cm as in all the above calculations unit cm is used so answer is in cm only. Keep in mind the units.