An object is placed at a distance of (f / 2) the from a convex lens the image will be.... (A) at

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An object is placed at a distance of (f / 2) the from a...

An object is placed at a distance of $(\mathrm{f} / 2)$ the from a convex lens the image will be....
(A) at $\mathrm{f}$, real and inverted
(B) at,$(3 \mathrm{f} / 2)$ real and inverted
(C) at one of the foci, virtual and double its size
(D) at $2 \mathrm{f}$, virtual and erect.

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Key Concepts

Virtual Image Formation and Magnification

When an object is placed closer to a convex lens than its focal length (i.e., do < f), the lens formula yields a negative image distance, indicating that the image is virtual and appears on the same side of the lens as the object. Additionally, the magnification formula (m = -di/do) shows that the image is magnified and upright, highlighting the typical behavior of convex lenses in such scenarios.

Convex Lens Behavior

A convex lens converges the incoming light and can form different types of images depending on the object's position relative to its focal length. When the object is beyond the focal point, a real and inverted image is formed; however, when the object is placed within the focal length, the lens produces a virtual, upright, and magnified image as the light rays diverge after refraction.

Lens Formula

The lens formula, given by 1/f = 1/do + 1/di (where f is the focal length, do is the object distance, and di is the image distance), is crucial in relating the distances involved in lens imaging. It allows us to calculate whether an image is real or virtual by determining the sign and magnitude of the image distance.

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