An object is placed at a distance 24 cm in front of a convex lens of focal length 8 cm.
Calculate the magnification of the image.
Topic: Lenses and image formation
Answer
Given: v = +12 cm (from part (ii)), u = −24 cm
Magnification, m = v ÷ u = (+12) ÷ (−24) = −0.5
Magnification = −0.5
The negative sign shows the image is inverted, and the size 0.5 shows it is half as tall as the object (diminished).
Keep the signs all the way through. The minus sign is not decoration — it is the part of the answer that tells you the image is inverted, and dropping it loses information the examiner is looking for.
For a lens the formula is m = v/u. Do not use the mirror version m = −v/u; they differ by a sign because the sign conventions for the two are set up differently.
Read the answer back in words: negative means inverted, and a magnitude below 1 means smaller than the object. So the image is real, inverted and half-size — exactly what a convex lens gives for an object beyond 2F.