Lenses, Mirrors, and Image Formation

Objective: Locate a virtual image and distinguish it from a projected image.

A plane mirror produces an image that appears the same perpendicular distance behind the mirror as the object is in front in the ideal ray model. Reflected rays do not actually converge behind the mirror; their backward extensions meet at the virtual image location. The image is upright and has the same size in this simple model. A virtual image can be seen by an observer but cannot be projected onto a screen placed at its apparent location without additional optics. Left–right reversal language can be misleading; the geometry reverses the front–back direction relative to the mirror. Image location should be described with distances measured perpendicular to the mirror.

Objective: Use principal rays and qualitative focal-distance cases.

A converging lens bends paraxial incoming parallel rays toward a focal point in the thin-lens model. If an object is beyond the focal length, the lens can form a real inverted image on the opposite side, projectable onto a screen. If the object lies inside the focal length, the outgoing rays diverge and their backward extensions give an upright magnified virtual image. The thin-lens relation 1/f = 1/d_o + 1/d_i applies with a consistent sign convention and paraxial approximation. For f = 10 cm and d_o = 20 cm, d_i = 20 cm. Real lenses have aberrations and wavelength-dependent behavior, so ray diagrams are models.

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.