Concave & Convex Mirrors

What are Curved Mirrors?

Curved mirrors have a spherical reflecting surface. A concave mirror curves inward (like a cave), converging light rays. A convex mirror curves outward, diverging light rays. The center of curvature (C) is the center of the sphere, and the focal point (F) is halfway between C and the mirror.

Mirror Equation

Where f = focal length, u = object distance, v = image distance. For concave mirrors f is positive; for convex mirrors f is negative. Magnification: m = -v/u.

Ray Diagrams

Three standard rays determine the image:

• Parallel Ray — parallel to axis, reflects through F
• Focal Ray — through F, reflects parallel to axis
• Central Ray — through C, reflects back on itself

Real vs Virtual Images

Real images form where rays actually meet — they are inverted and can be projected on a screen. Virtual images form where rays appear to come from — they are erect and cannot be projected. Concave mirrors can form both; convex mirrors always form virtual images.

Applications

• Concave: Telescopes, shaving mirrors, car headlights, solar concentrators
• Convex: Rear-view mirrors, security mirrors (wider field of view)

Key Points

• For concave mirrors, objects beyond C produce real, inverted, diminished images
• Objects at C produce same-size, inverted images at C
• Objects between F and C produce real, inverted, enlarged images
• Objects at F produce no image (rays emerge parallel)
• Objects between F and pole produce virtual, erect, enlarged images
• Convex mirrors always produce virtual, erect, diminished images