Mirrors and Lenses

Objective: Compare image outcomes and avoid universal mirror claims.

A diverging lens causes incoming parallel rays to spread, appearing to originate from a focal point on the incident side; a real object normally produces an upright, reduced virtual image under the thin-lens model. A concave mirror can converge parallel rays and form real or virtual images depending on object distance relative to focal length, while a convex mirror produces an upright, reduced virtual image for ordinary real objects. Image size and orientation cannot be inferred from “mirror” or “lens” alone. Curved-mirror equations use consistent sign conventions and approximations; a ray diagram often gives a useful qualitative answer first. The geometry of reflection differs from refraction through a lens.

Objective: Apply mirrors and lenses to calculations, evidence, and specified situations.

For a thin lens in the paraxial model, 1/f=1/d_o+1/d_i and signed magnification is −d_i/d_o. In the stated convention, a real object has positive d_o, a converging lens positive f, and a diverging lens negative f. Positive d_i indicates a real image on the opposite side; negative d_i a virtual image on the object side. Negative magnification indicates inversion. Curved mirrors have related paraxial image equations but require their stated mirror sign convention; do not transfer signs without checking.