Lens Displacement and u-v Experiments
For object-screen distance D and separation d between conjugate lens positions, f = (D^2-d^2)/(4D), provided D > 4f and the lens is thin.
Why this shows up in the exam
School focal-length experiments · Lens testing · Conjugate-image measurements
Learn the idea
A fixed object-screen distance greater than four focal lengths can give two sharp convex-lens positions. Swapping the roles of object and image distances preserves the same total separation, creating two conjugate positions.
🧠 Memory hook: Two sharp positions exist only beyond 4f.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- f = (D²-d²)/(4D) — Bessel displacement method
- D_min = 4f — minimum object-screen separation for a sharp real image
How to approach it
- 1Confirm D > 4f or two positions
- 2Measure D and d distinctly
- 3Substitute into the displacement formula
Common slip-ups that cost marks
- •Using the method for a concave lens alone
- •Confusing D with lens displacement d
- •Ignoring the real-image screen requirement
🌟 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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