An object placed 50cm from a lens produces a virtual image at a distance of 10cm from the lens. What is the focal length of the lens and also state the type of lens used?

An object placed

50 cm

from a lens produces a virtual image at a distance of

10 cm

from the lens. The Focal length of the lens,

f = - 12.5 cm

The type of lens is Concave.
Given data,
Distance of the object from the lens,

u = - 50 cm

Distance of the virtual image from the lens,

v = - 10 cm

So,

\frac{1}{f} = \frac{1}{v} - \frac{1}{u}

⇒

\frac{1}{f} = \frac{1}{- 10} - \frac{1}{- 50}

= - \frac{1}{10} + \frac{1}{50}

= \frac{- 5 + 1}{50}

= - \frac{4}{50}

⇒

f = - \frac{50}{4}

⇒

f = - 12.5 cm

Thus, the focal length of the lens is

- 12.5 cm

, and the lens is concave.

An object placed $50 cm$ from a lens produces a virtual image at a distance of $10 cm$ from the lens. What is the focal length of the lens and also state the type of lens used?