An object 4 cm tall is placed 15 cm from a convex lens of focal length 10 cm. (a) Draw a ray diagram. (b) Find the position, size and nature of the image. (c) Find the power of the lens.

1. 1 · Write what is given, with signs. u = −15 cm, f = +10 cm (convex), object height O = 4 cm.
2. 2 · Write the lens formula. 1/f = 1/v − 1/u, so 1/v = 1/f + 1/u.
3. 3 · Solve for v. 1/v = 1/10 − 1/15 = (3 − 2)/30 = 1/30, so v = +30 cm.
4. 4 · Find m and the image height. m = v/u = 30/(−15) = −2, so I = −2 × 4 cm = −8 cm.
5. 5 · Find the power. f = 0.10 m, so P = 1/0.10 = +10 D.
6. 6 · Draw the ray diagram. [Sketch: object between F₁ and 2F₁; parallel ray through F₂; ray through O straight; they meet beyond 2F₂, below the axis]
7. 7 · State the result. Image 30 cm on the far side; real, inverted, 8 cm tall (twice the object). Power +10 D.

Scoring tip: Convert f to metres only for power. Keep cm for the lens formula, but use the same unit for u, v and f.