5.4 Images from Mirrors

The Mirror Equation

For both concave and convex mirrors, image location follows 1/f = 1/d₀ + 1/dᵢ, where f is focal length, d₀ is object distance, and dᵢ is image distance. Focal length relates to radius of curvature by f = R/2. Concave mirrors have positive f; convex mirrors have negative f, since their focal point is virtual (behind the mirror).

Magnification and Image Properties

Magnification m = -dᵢ/d₀ = hᵢ/h₀ tells you size and orientation. Negative m means inverted; positive means upright. A negative dᵢ signals a virtual image (behind the mirror), while positive dᵢ means a real image (in front, projectable). Convex mirrors always form upright, virtual, reduced images.

Ray Diagrams

Locate images using principal rays: one parallel to the axis reflects through the focal point; one through the focal point reflects parallel; one through the center of curvature reflects straight back. Where reflected rays intersect (or appear to intersect) gives the image location — real if rays actually converge, virtual if only their extensions meet.

Key terms

Mirror equation

1/f = 1/d₀ + 1/dᵢ, relating focal length, object distance, and image distance.

Magnification formula

m = -dᵢ/d₀ = hᵢ/h₀; negative means inverted, positive means upright.

Focal length vs radius of curvature

f = R/2 — the focal point lies halfway between the mirror and center of curvature.

Concave mirror image (object beyond C)

Real, inverted, reduced image formed between F and C.

Convex mirror images

Always virtual, upright, and reduced, regardless of object position.

Try an AP-style question

A concave mirror has radius of curvature 40 cm. What is its focal length?

1. 20 cm
2. 10 cm
3. 80 cm
4. 40 cm