An object is placed 12 cm away from the optical centre of a lens Its image is formed exactly midway between the optical centre and the object. Wht is the nature of lens and its focal length.

We have,

Object distance, u = -12 cm

Image distance = v

Focal length = f

Since, the image is formed midway between the lens and the object,

So, v = -6 cm

Now,

1/f = 1/v – 1/u

=> 1/f = -1/6 + 1/12

=> 1/f = -1/12

=> f = -12 cm

Thus, it is a concave lens producing a virtual image on the same side of the object.