An object is placed 30 cm from a convex lens of focal length 20 cm. Find the position and nature of the image, and the power of the lens.

How to lay out the answer. Follow the frame, then write it in your own words.

1 · Write the formulas. Lens formula: 1/f = 1/v − 1/u; magnification m = v/u; power P = 1/f.
2 · Write the given values with signs. u = −30 cm, f = +20 cm (Cartesian sign convention).
3 · Find v. 1/v = 1/20 − 1/30 = 1/60, so v = +60 cm.
4 · Find m and the nature of the image. m = 60/(−30) = −2: real, inverted, magnified two times.
5 · Find the power. f = 0.2 m, so P = 1/0.2 = +5 D.
6 · Real-life link. Spectacle prescriptions give the power of each lens in dioptres.
7 · Close in one line. The image is 60 cm behind the lens, real and inverted, and the lens has a power of +5 D.

Scoring tip: Put the signs into u, v and f before you substitute. Change centimetres to metres before finding the power.