Optical Power and Lenses in Contact
In air for thin coaxial lenses in contact, P_eq = sum(P_i), where P = 1/f in metres and is measured in dioptres.
Why this shows up in the exam
Spectacle prescriptions · Close-up lens attachments · Compound lens estimation
Learn the idea
Thin lenses in contact add their optical powers. Successive thin lenses at nearly the same plane add convergence or divergence without appreciable propagation between them.
🧠 Memory hook: Contact lenses add powers, not focal lengths.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- P = 1/f(m) — lens power in dioptres
- P_eq = P1 + P2 + ... — thin lenses in contact
How to approach it
- 1Convert focal lengths to metres
- 2Assign power signs
- 3Add powers and invert if focal length is requested
Common slip-ups that cost marks
- •Adding focal lengths
- •Using centimetres in P = 1/f
- •Ignoring the sign of a concave lens
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A real object is placed 30 cm from a converging lens of focal length 10 cm. Find the real image distance.
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