An optician prescribes spectacle lenses of power +2.0 D for one eye and –0.5 D for the other. (i) What is the focal length of each lens? (ii) What type is each lens? (iii) If both lenses were placed in contact, what would be the power of the combination?
Generated by claude-sonnet-4-6 · 2026-06-26 01:12 · grounding rag
Model Answer
(i) Focal length of each lens:
Using $P = \dfrac{1}{f}$, so $f = \dfrac{1}{P}$
- For +2.0 D: $f = \dfrac{1}{+2.0} = +0.5 \text{ m}$
- For –0.5 D: $f = \dfrac{1}{-0.5} = -2.0 \text{ m}$
(ii) Type of each lens:
- Lens with power +2.0 D is a convex (converging) lens (positive power).
- Lens with power –0.5 D is a concave (diverging) lens (negative power).
(iii) Power of combination:
$$P = P_1 + P_2 = (+2.0) + (-0.5) = +1.5 \text{ D}$$
The combination acts as a convex lens of power +1.5 D.
Source: Chapter 9, Section 9.3.8 Power of a Lens
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Explanation
- The key formula is $f = 1/P$ (with $f$ in metres and $P$ in dioptres).
- Examiners expect you to state the sign and type of lens — positive power = convex, negative power = concave.
- For the combination, simply add powers algebraically: $P = P_1 + P_2$. Always state what type of lens the resultant power represents.
- Common mistake: forgetting to express focal length in metres, not centimetres.