An object 3 cm tall is placed 12 cm from a convex lens of focal length 8 cm. Find the position, size and nature of the image, and the power of the lens.

1. 1 · Write what is given, with signs. h = +3 cm, u = −12 cm, f = +8 cm (convex lens).
2. 2 · Write the lens formula. 1/v − 1/u = 1/f, so 1/v = 1/f + 1/u.
3. 3 · Substitute and solve for v. 1/v = 1/8 + 1/(−12) = (3 − 2)/24 = 1/24, so v = +24 cm.
4. 4 · Find m and h′. m = v/u = 24/(−12) = −2; h′ = m × h = −2 × 3 cm = −6 cm.
5. 5 · Find the power. f = +8 cm = +0.08 m, so P = 1/0.08 = +12.5 D.
6. 6 · Sketch the ray diagram. [Sketch: object between F₁ and 2F₁; rays meet beyond 2F₂; inverted, larger image]
7. 7 · State the result and a use. Image 24 cm on the other side: real, inverted, 6 cm tall (twice the size). A slide projector uses a convex lens this way.
8. 8 · Box the answers. v = +24 cm, m = −2, h′ = −6 cm, P = +12.5 D.

Scoring tip: Change the focal length to metres before finding power, and write the unit D after the number.