An object placed 60 cm from a lens gives a virtual image 20 cm in front of the lens (on the same side as the object). What is the focal length, and what type of lens is it?

1. Sign convention: object on left u = −60 cm; virtual image on the same side v = −20 cm. 2. $\frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{-20} - \frac{1}{-60} = -\frac{1}{20} + \frac{1}{60}$. 3. $\frac{1}{f} = \frac{-3 + 1}{60} = \frac{-2}{60} = -\frac{1}{30}$. 4. So f = −30 cm; the negative focal length means a diverging (concave) lens. Taking v as +20 cm would wrongly give a convex result. _Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 7 "Lenses", p.101_