A convex lens has a focal length of 15 cm. At what distance should an

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 ?

15 cm
10 cm
30 cm
40 cm
This question was previously asked in
UPSC CDS-1 – 2022
An object should be placed at a distance of 30 cm from the convex lens.
For a convex lens, a real image of the same size as the object is formed when the object is placed at a distance equal to twice the focal length (2f) from the lens. At this position (often referred to as 2F or C), the image is also formed at a distance of 2f on the opposite side of the lens, and it is real, inverted, and of the same size as the object. Given the focal length (f) is 15 cm, the object distance required is 2 * f = 2 * 15 cm = 30 cm.
Placing the object at the focal length (15 cm) results in an image at infinity. Placing the object between the focal length and the lens results in a virtual, erect, and magnified image. Placing the object beyond 2f results in a real, inverted, and diminished image.