A convex lens forms a real image of an object for it s two...

A convex lens forms a real image of an object for it s two different positions on a screen if height of the image in both cases be $16 \mathrm{~cm}$ and $4 \mathrm{~cm}$ then height of the object is $\quad \mathrm{cm}$.
(A) $-4$
(B) 4
(C) $-8$
(D) 8

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Key Concepts

Dual Image Formation and Product of Magnifications

When a convex lens is adjusted to form a real image on a fixed screen from two different lens positions, the object and image distances obey a quadratic relationship with a constant sum. In such a scenario, the magnifications from both positions turn out to be reciprocal, meaning their product is unity. This property provides an elegant way to relate the known image heights to the unknown object height.

Magnification

Magnification in optics is defined as the ratio of the image height to the object height, and it is also related to the ratio of the image distance to the object distance (m = v/u). This concept helps in understanding how much larger or smaller an image is compared to the original object.

Lens Formula

The lens formula, expressed as 1/f = 1/u + 1/v, connects the focal length of a lens with the object distance (u) and the image distance (v). This relationship is fundamental in geometrical optics for determining where an image will form and its characteristics.

Convex Lens

A convex lens is a converging optical device that primarily produces real, inverted images when the object is placed outside its focal point. Its behavior is governed by its ability to bring parallel rays to a convergent point, known as the focal point, and is essential for forming sharp images on a screen.

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