Light — Reflection and Refraction

Reflection by plane and spherical mirrors, refraction and refractive index, lenses, the mirror and lens formulas, and the power of a lens.

Key ideas

Laws of reflection: the angle of incidence equals the angle of reflection, and both rays and the normal lie in one plane.
For spherical mirrors, the focal length is half the radius of curvature.
Sign convention: measure all distances from the pole (or optical centre); along the incident light is positive, against it negative; heights above the axis are positive.
A concave mirror and a convex lens converge light; a convex mirror and a concave lens spread it out.
Light bends towards the normal when it slows down entering a denser medium.
Refractive index compares the speed of light in a vacuum (or air) with its speed in the medium.
The power of a lens is 1 ÷ f with f in metres; convex lenses have positive power, concave lenses negative.

Forgetting the sign convention: an object in front of a mirror or lens has a negative u.
Using the mirror formula for a lens (the lens formula has a minus sign).
Using f in centimetres when finding the power of a lens.

Where should an object be placed in front of a convex lens of focal length 9 cm to get a real image the same size as the object?

Working: m = v/u = −1, so v = −u; 1/v − 1/u = 1/9 gives u = −18 cm, v = 18 cm

Answer: 18 cm from the lens (u = −18 cm)