Question

An object is placed in front of a convex lens of focal length 12 cm. If the size of the real image formed is half the size of the object, calculate the distance of the object from the lens.

Answer 1

In the given problem,
Focal length of a concave lens, f = 12 cm
(using sign convention )
height of the image `(h_(i)) = 1/2 xx" height of the object "(h_(o))`
i.e., `h_(i) = 1/2 h_(o)`.
Magnification of the lens ` m = v/n = h_(i)/h_(o)`
v is the image distance
u is the object distance.
` m = h_(i)/h_(o) = 1/2 h_(o)/h_(o) = 1/2 `
` m = v/ n`
` 1/2 = v/u`
` rArr v = u/2`
From lens formula.
` 1/f = 1/v - 1/u`
` 1/(12) = 1/(u/2) - 1/u`
` 1/(12) = 2/u + 1/u`
` 1/12 = (2+1)/u`
` 1/12 = 3/u`
u = 36 cm.
The object is placed at a distance of 36 cm from the lens.