A pencil is placed upright at a distance of- 10 cm from a convex lens of focal length 15 cm. The nature of the image of the pencil will be

In this scenario, a pencil (object) is placed at a distance (u) of 10 cm from a convex lens with a focal length (f) of 15 cm. According to the sign convention, u = -10 cm and f = +15 cm. Using the lens formula (1/f = 1/v - 1/u), we find 1/v = 1/15 + 1/(-10), which results in v = -30 cm. Since the image distance (v) is negative, the image is formed on the same side as the object, making it virtual. For a convex lens, when an object is placed between the optical centre and the principal focus (u < f), the refracted rays diverge and appear to meet behind the object. This specific configuration always results in an image that is virtual, erect, and magnified. The magnification (m = v/u) is +3, confirming the image is three times larger than the pencil.