A point object P is placed at centre of curvature of a...

A point object $P$ is placed at centre of curvature of a concave mirror of focal length $25 \mathrm{~cm}$. The mirror is cut into two halves and shifted symmetrically $1 \mathrm{~cm}$ apart in perpendicular to the optical axis. The distance between images formed by both parts is: (a) $2 \mathrm{~cm}$ (b) $1 \mathrm{~cm}$ (c) $3 \mathrm{~cm}$ (d) $4 \mathrm{~cm}$

A point object $P$ is placed at centre of curvature of a concave mirror of focal length $25 \mathrm{~cm}$. The mirror is cut into two halves and shifted symmetrically $1 \mathrm{~cm}$ apart in perpendicular to the optical axis. The distance between images formed by both parts is:
(a) $2 \mathrm{~cm}$
(b) $1 \mathrm{~cm}$
(c) $3 \mathrm{~cm}$
(d) $4 \mathrm{~cm}$

Key Concepts

Image Formation by Concave Mirrors

Understanding how concave mirrors form images involves analyzing the paths of reflected rays and applying the mirror equation. When an object is placed at the centre of curvature, the reflected rays converge to form an image at the same point as the object, serving as a foundation for more complex situations when the mirror is altered or displaced.

Effect of Lateral Displacement of Optical Elements

When a mirror or part of a mirror is laterally shifted, the corresponding image shift is influenced by this displacement. Specifically, a lateral shift in the mirror leads to a doubled displacement in the image position due to the law of reflection. This effect is critical in problems where mirror segments are separated or translated, as it determines the relative positions of images formed by the displaced components.

Concave Mirror Geometry

This concept deals with the basic geometry and properties of concave mirrors, including the relationships between the focal length, the centre of curvature, and the vertex. A concave mirror forms images based on the object's position relative to these key points, following the mirror equation and ray diagrams.

Focal Length and Centre of Curvature Relationship

A critical idea in mirror optics is the relationship between the focal length and the centre of curvature; the centre of curvature is twice the focal length. This relationship is essential in determining the position and nature of the image formed by a concave mirror when an object is placed at strategic points, such as its centre of curvature.

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