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

A dentist holds a concave mirror of focal length 6 cm at 4 cm from a tooth 0.5 cm tall. Find the position, nature and size 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. h = +0.5 cm, u = −4 cm, f = −6 cm (concave, so f is negative).
  2. 2 · Write the mirror formula. 1/v + 1/u = 1/f, so 1/v = 1/f − 1/u.
  3. 3 · Substitute and solve for v. 1/v = −1/6 + 1/4 = (−2 + 3)/12 = 1/12, so v = +12 cm.
  4. 4 · Find m and h′. m = −v/u = −(12)/(−4) = +3; h′ = m × h = 3 × 0.5 = +1.5 cm.
  5. 5 · Sketch the ray diagram to check. [Sketch: tooth between P and F; dotted rays meet behind the mirror; erect, larger image]
  6. 6 · State the result and why it helps. Image 12 cm behind the mirror, virtual, erect and 1.5 cm tall (three times larger), so the dentist sees the tooth clearly.
  7. 7 · Box the answers with units. v = +12 cm, m = +3, h′ = +1.5 cm.

Scoring tip: Write the sign with every value before you substitute. Most lost marks come from a missing minus sign.