Refraction of Light and Lenses
Refraction of Light and Lenses tests Snell's law, refractive index, image formation by convex and concave lenses, lens formula, magnification and power. Ray diagrams and sign conventions must agree with the calculation.
Core rules
- Refraction is bending of light when it changes speed between media. Refractive index n = c/v, where c is speed in vacuum. n has no unit.
- Snell's law: n1 sin i = n2 sin r. Light bending towards the normal enters a denser medium.
- A convex lens is converging and can form real or virtual images; a concave lens is diverging and forms virtual, diminished images for real objects.
- Cartesian sign convention: distances measured in the direction of incident light are positive; opposite are negative. Lens formula: 1/v - 1/u = 1/f. Magnification m = v/u = h'/h.
- Power P = 1/f with f in metres; unit is dioptre (D). Convex power is positive, concave negative.
Worked example
An object is 20 cm from a convex lens of focal length 10 cm. Using u = -20 cm and f = +10 cm: 1/v - 1/u = 1/f, so 1/v - 1/(-20) = 1/10. Thus 1/v + 1/20 = 1/10, giving 1/v = 1/20 and v = +20 cm. The image is real, on the opposite side, and m = v/u = 20/(-20) = -1, so it is inverted and same size.
Traps
Do not ignore signs for u, v and f. A positive image distance does not always mean a real image unless the convention is applied. Power uses focal length in metres, not centimetres. Refractive index is a ratio, so it has no unit. Do not draw a ray through the optical centre bending away from its straight path.