Cut Lenses, Aperture and Image Brightness
For a thin lens cut parallel to its principal axis, each piece retains focal length while aperture and image intensity decrease; a cut perpendicular to the axis changes a surface and therefore power.
Why this shows up in the exam
Split-aperture imaging · Lens fabrication · Brightness control
Learn the idea
Cutting a thin lens changes aperture or surface curvature depending on the cut, but does not automatically change every optical property. A cut parallel to the principal axis keeps each piece's curvatures and focal length but reduces collected light and shifts its optical centre.
🧠 Memory hook: Ask what the cut changes: curvature, aperture, or centre.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- P = (n-1)(1/R1-1/R2) — use actual surfaces after the cut
- intensity roughly proportional to aperture area — same illumination and negligible losses
How to approach it
- 1Identify the cut plane
- 2List retained surface curvatures
- 3Separate focal length, image position and brightness effects
Common slip-ups that cost marks
- •Halving focal length for every cut
- •Saying half a lens gives half an image
- •Ignoring image displacement from an off-axis piece
🌟 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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