A convex lens has a focal length of 15 cm. At what distance should an object be placed in front of the lens to get a real image of the same size of the object ?

For a convex (converging) lens, the nature and size of the image depend on the object's position relative to the focal length (f). According to the lens properties, when an object is placed at a distance equal to twice the focal length (2f), the image formed is real, inverted, and of the same size as the object. This specific condition occurs because at u = 2f, the lens formula (1/v - 1/u = 1/f) results in an image distance (v) also equal to 2f, leading to a magnification (m = v/u) of 1. In this problem, the focal length (f) is given as 15 cm. Therefore, to obtain a real image of the same size, the object must be placed at 2f, which is 2 × 15 cm = 30 cm.

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction > Activity 9.12 > p. 152