Separated Thin Lenses and Equivalent Focal Length
For two thin lenses in air separated by d, P_eq = P1 + P2 - d P1 P2 with d in metres; direct sequential imaging also gives final image position.
Why this shows up in the exam
Zoom-system modelling · Relay optics · Lens-pair focal calculations
Learn the idea
Separation between lenses changes the equivalent power because rays propagate before meeting the second lens. The first lens creates an intermediate image that serves as the object for the second.
🧠 Memory hook: With a gap, add powers and subtract d P1 P2.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- P_eq = P1 + P2 - d P1 P2 — equivalent power of two separated thin lenses in air
- u2 = x_image1 - x_lens2 — coordinate transfer to the second lens
How to approach it
- 1Choose a common coordinate axis
- 2Image through the first lens
- 3Use that coordinate as the second lens object or apply equivalent power
Common slip-ups that cost marks
- •Using the contact formula
- •Mixing centimetres and metres
- •Treating equivalent focal length as final image distance for every object
🌟 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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