Lenses: Image Formation and Formula Explained for School

A lens is a transparent piece of glass or plastic with curved surfaces that refracts light to form images. Convex lenses converge rays, concave lenses diverge them. With a simple formula we can predict image position, size and nature for any object placement.

Lenses are everywhere: spectacles correct vision, cameras capture photos, microscopes reveal tiny worlds. Learning image formation by lenses gives you the tools to understand all these devices and solve school problems confidently.

Key Concepts

Convex (converging) lens: Thicker at centre, focal length positive. Concave (diverging) lens: Thinner at centre, focal length negative in Cartesian convention.

Principal focus F and focal length f: Point where parallel rays meet (or appear to meet). f in metres or centimetres.

Optical centre: Central point through which ray passes undeviated.

• Real image formed by actual meeting of rays on opposite side
• Virtual image on same side as object, cannot be caught on screen
• Ray rules: parallel ray through focus, ray through centre straight, ray through focus becomes parallel

Formulas

Lens formula: 1 divided by f = 1 divided by v minus 1 divided by u in Cartesian sign convention (light left to right). Equivalent form 1 divided by f = 1 divided by v plus 1 divided by u in other convention. f, v, u in metres with sign.

Magnification m = v divided by u = height image divided by height object in Cartesian (with sign). In magnitude form, m = image distance divided by object distance.

Assumes thin lens, paraxial rays, lens in air.

Worked Example

Convex lens f = +20 cm. Object 30 cm left of lens (u = minus 30 cm in Cartesian). Find image.

1. Use 1 divided by f = 1 divided by v minus 1 divided by u, so 1 divided by 20 = 1 divided by v minus 1 divided by minus 30 = 1 divided by v plus 1 divided by 30.
2. Thus 1 divided by v = 1 divided by 20 minus 1 divided by 30 = 1 divided by 60.
3. v = +60 cm, 60 cm to right, real image.
4. m = v divided by u = 60 divided by minus 30 = minus 2. Image inverted, twice enlarged.

Object between F and 2F gives real, inverted, enlarged image beyond 2F, as used in projectors.

Common Misconceptions

• Concave lens forms real image: In usual cases concave lens always forms virtual, erect, diminished image for real object.
• Image always on opposite side: Virtual images for convex lens when object inside focal length appear on same side, used as magnifying glass.
• Focal length changes with object distance: f is fixed for a lens (in given medium). Image distance changes, not f.

Real-World Applications

• Spectacles and contact lenses correct myopia and hypermetropia with concave and convex lenses
• Camera lenses focus real inverted image onto sensor
• Magnifying glass is convex lens with object inside f giving erect virtual enlarged image
• Microscopes and telescopes combine lenses for high magnification

Lens formula and ray rules let you locate images for any setup. Place object, apply rules, compute m, and you know size, orientation and whether image is real or virtual.