Two convex lenses P and Q have focal lengths 10 cm and 40 cm respectively. (a) Calculate the power of each lens. (b) A parallel beam of light falls on each lens separately. For which lens will the refracted rays converge closer to the lens, and why? (c) If these two lenses are placed in contact, what is the power of the combination? What type of lens does this combination behave like?
Generated by claude-sonnet-4-6 · 2026-06-26 01:16 · grounding rag
Model Answer
(a) Power of each lens:
$$P_P = \frac{1}{f_P} = \frac{1}{0.10 \text{ m}} = +10 \text{ D}$$
$$P_Q = \frac{1}{f_Q} = \frac{1}{0.40 \text{ m}} = +2.5 \text{ D}$$
(b) Lens P (focal length 10 cm) will converge the parallel beam closer to the lens. A convex lens of shorter focal length bends light rays through larger angles, focusing them nearer to the optical centre.
(c) Power of combination:
$$P = P_P + P_Q = 10 + 2.5 = +12.5 \text{ D}$$
Since the combined power is positive, the combination behaves like a convex (converging) lens.
Source: Chapter 9, Section 9.3.8 — Power of a Lens
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Explanation
- Always convert focal length to metres before calculating power.
- Both lenses are convex → positive focal lengths → positive powers.
- Key concept: shorter focal length = higher power = stronger convergence (rays focus closer).
- For combined power, simply add individual powers algebraically; positive result → convex behaviour. Examiners expect you to state both the numerical value and the lens type.