When a convex lens produces a real image of an object, the minimum distance between the object and image is equal to

For a convex lens to produce a real image, the object must be placed beyond the focal point. The distance between the object and its real image is given by the sum of the object distance (u) and the image distance (v). According to the lens formula, 1/f = 1/v - 1/u. By applying the sign convention where u is negative, the total distance D = |u| + v can be expressed as a function of u and f. Mathematically, the minimum value of this distance occurs when the object is placed at a distance of 2f from the optical center. In this specific configuration, the image is also formed at 2f on the opposite side of the lens [1]. Consequently, the total minimum distance between the object and the real image is 2f + 2f, which equals 4f, or four times the focal length.

Sources

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