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Sign convention, mirror formula and magnification sheet
3-mark answer frame

A concave mirror has a radius of curvature of 40 cm. An object 5 cm tall is placed 30 cm in front of it. Find the position, size and nature of the image.

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

  1. 1 · Write what is given, with signs. R = 40 cm, so f = −20 cm (concave). u = −30 cm. Object height O = 5 cm.
  2. 2 · Write the mirror formula. 1/f = 1/v + 1/u, so 1/v = 1/f − 1/u.
  3. 3 · Substitute and solve. 1/v = −1/20 + 1/30 = (−3 + 2)/60 = −1/60, so v = −60 cm.
  4. 4 · Find the magnification and image size. m = −v/u = −(−60)/(−30) = −2, so I = m × O = −2 × 5 cm = −10 cm (inverted).
  5. 5 · Check with a quick sketch. [Sketch: object between C and F; rays meet beyond C, below the axis]
  6. 6 · State the result. Image 60 cm in front of the mirror; real, inverted, 10 cm tall (twice the object).

Scoring tip: Write the sign with every value before you substitute. A missing minus sign is the commonest lost mark.