Thin lenses

Types

• Converging (convex): thicker in the middle; brings rays to a real focus.
• Diverging (concave): thinner in the middle; spreads rays out.

Lens formula (real-is-positive)

1/f = 1/u + 1/v

• u: object distance; v: image distance; f: focal length.
• Virtual image distances are negative; diverging lenses have negative f.

Example: Object 30 cm from a lens of f = 10 cm: 1/v = 1/10 - 1/30 = 2/30 → v = 15 cm (real).

Magnification

m = v ÷ u = image height ÷ object height. In the example, m = 15/30 = 0.5.

Power of a lens

P = 1/f (f in metres), measured in dioptres (D). f = 25 cm → P = +4 D.

Images by a convex lens

• Object beyond 2F: real, inverted, diminished (camera).
• Object at 2F: real, inverted, same size.
• Between F and 2F: real, inverted, magnified (projector).
• Inside F: virtual, upright, magnified (magnifying glass).

Defects of vision

• Short sight (myopia): corrected with a concave lens.
• Long sight (hypermetropia): corrected with a convex lens.