A convex lens forms an inverted image of size same as that of the object which is placed at a distance 60 cm in front of the lens.

Find —

(a) The position of image, and

(b) The focal length of the lens

An inverted, real and same size image of an object, is formed by a convex lens when the object is placed at 2f i.e. u = 2f₁.

(a) When the object is at 2f₁ in a convex lens then the image is formed at 2f₂. Hence, position of the image is 60 cm behind the lens.

(b) To find the focal length of this lens, we use the relationship given below,

Object distance (u) = 2f

Given,

Object distance (u) = 60 cm

Using the two equivalent values we get,

$60 = 2 \times f \\[0.5em] f = \dfrac{60}{2} \\[0.5em] \Rightarrow f = 30 \\[0.5em]$

Therefore, the focal length of the given lens is 30 cm