A `2.0 cm` tall object is placed perpendicular to the principal axis of a convex lens of focal length 10 cm. The distance of the object from the lens is 15 cm. Find the nature, position and size of the image. Also, find its magnification.

Explanation

Here, object size, `h_(1) = 2.0 cm`, focal length of convex lens, `f = 10 cm`
object distance, `u -15 cm`, Image distance, `v = ?`, Image size, `h_(2) = ?`
As `1/v - 1/u = 1/f, 1/v = 1/f + 1/u = 1/10 - 1/15 = 1/30`
or `v = 30 cm`.
As v is positive, the image formed is on the right side of the lens. It must be real and inverted.
As linear magnification, `m = (h_(2))/(h_(1)) = v/u, (h_(2))/(2.0) = 30/(-15) = -2`
or ` h_(2) = -4.0 cm`.
Negative sign of m and `h_(2)` show that the image is inverted.
Thus a real, inverted image enlarged 2 times (i.e. `4.0 cm` tall) is formed at a distance of `30 cm` on the right side of the lens.