Light: Reflection and Refraction
Light: Reflection and Refraction examines mirror and lens formulae, sign conventions and refractive index. Most lost marks come from signs, not from algebra.
Reflection and mirrors
- Angle of incidence equals angle of reflection, and the incident ray, reflected ray and normal lie in one plane.
- For a spherical mirror, 1/v + 1/u = 1/f with the Cartesian sign convention. Focal length of a spherical mirror is half its radius of curvature: f = R/2.
- Magnification m = -v/u for mirrors. A negative m means an inverted image.
Refraction and lenses
- Refraction is bending due to a change of speed when light crosses a boundary. Snell's law: n = sin i / sin r for light entering a medium from air.
- A convex lens converges light and can form real or virtual images; a concave lens diverges light.
- Lens formula: 1/v - 1/u = 1/f, again with signs. Magnification m = v/u.
Worked example
An object is 15 cm from a concave mirror of focal length 10 cm. Use u = -15 cm and f = -10 cm. 1/v + 1/(-15) = 1/(-10), so 1/v = 1/15 - 1/10 = (2 - 3)/30 = -1/30. Thus v = -30 cm: the image is real, inverted and 30 cm in front of the mirror. Magnification m = -v/u = -(-30)/(-15) = -2.
Traps
- Mixing sign conventions between mirrors and lenses.
- Treating a virtual image distance as positive when the convention says negative.
- Writing n = sin r / sin i instead of sin i / sin r.
- Assuming all convex-lens images are real; an object inside the focal length gives a virtual image.