A point object is placed at the centre of curvature of a spherical con

A point object is placed at the centre of curvature of a spherical concave mirror. Which one among the following would be the correct location of image formed ?

At infinity

At the centre of curvature

At the focal point

Between the focal point and the centre of curvature

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC NDA-2 – 2024

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For a spherical concave mirror, when an object is placed at the centre of curvature (C), the image formed is also located at the centre of curvature (C).

When the object is at the centre of curvature of a concave mirror, the image formed is real, inverted, and has the same size as the object. Ray diagrams show that rays from the object passing through the focal point become parallel after reflection, and rays hitting the mirror perpendicularly pass through the centre of curvature after reflection. These reflected rays intersect at the centre of curvature.

The relationship between object distance (u), image distance (v), and focal length (f) for a spherical mirror is given by the mirror formula: 1/f = 1/u + 1/v. For a concave mirror, f is positive. The centre of curvature (C) is located at a distance 2f from the pole of the mirror. If u = 2f (object at C), then 1/f = 1/(2f) + 1/v. Solving for 1/v gives 1/v = 1/f – 1/(2f) = 2/(2f) – 1/(2f) = 1/(2f). Thus, v = 2f, meaning the image is also formed at the centre of curvature.

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