In geometrical optics, convex mirrors (bulging outward) and concave mirrors (curving inward) are both examples of which type of mirrors commonly studied in ray diagrams?

Introduction / Context:

Convex and concave mirrors are standard elements in ray optics and appear in many textbook ray diagrams for image formation. To classify these mirrors correctly, you need to recall the shape of their reflecting surfaces and how they are related to simple geometric surfaces. This question tests whether you know the general name given to convex and concave mirrors based on their geometry.

Given Data / Assumptions:

• A convex mirror has a reflecting surface that bulges outward towards the object.
• A concave mirror has a reflecting surface that curves inward like the inside of a sphere.
• Both are standard mirrors used for focusing or spreading light in optical systems.
• We are to identify the common geometric category that includes both convex and concave mirrors.

Concept / Approach:

Convex and concave mirrors are formed by taking a section of a spherical surface and silvering either the outside or inside surface. Because the reflecting surface is part of a sphere, these mirrors are collectively called spherical mirrors. A plane mirror corresponds to a flat surface, not a curved one. Parabolic mirrors have surfaces shaped like a paraboloid, not a sphere, and are used where precise focusing is needed, for example in telescopes. Cylindrical mirrors have curvature in one direction only, unlike spherical mirrors which curve in all directions from the centre. Thus, convex and concave mirrors fall into the category of spherical mirrors.

Step-by-Step Solution:

Verification / Alternative check:

In standard ray optics chapters, you will see separate sections titled spherical mirrors, convex mirror and concave mirror. The formula for spherical mirrors relating object distance, image distance and focal length (the mirror formula) is written as 1 / f = 1 / v + 1 / u with sign conventions suitable for spherical mirrors. This formula does not apply to plane mirrors or parabolic mirrors in the same simple form, confirming that convex and concave mirrors are grouped as spherical mirrors.

Why Other Options Are Wrong:

Option A (plane mirrors): These have flat surfaces and are not derived from a sphere, so they are not classified as convex or concave spherical mirrors.

Option C (cylindrical mirrors): A cylindrical mirror curves in one direction only, like a segment of a cylinder, and is used for focusing light into a line, not a point.

Option D (parabolic mirrors): These have a parabolic shape and are used in telescopes and satellite dishes to focus parallel rays exactly at a point, but their curvature is not spherical.

Option E (corner reflector mirrors): This is a specific arrangement of plane mirrors at right angles, not a description of the curved surfaces of convex and concave mirrors.

Common Pitfalls:

Students sometimes confuse spherical mirrors with parabolic mirrors because both can focus light. In reality, spherical mirrors are easier to make but introduce spherical aberration, while parabolic mirrors are more precise but harder to manufacture. For basic school physics questions, convex and concave mirrors are treated as ideal spherical mirrors, and you should remember this classification for quick and accurate answers.

Final Answer:

Convex and concave mirrors are examples of spherical mirrors.