Lens-Mirror Systems and Retracing
Use sequential paraxial imaging with a fixed coordinate system. When an image lies at a spherical mirror's centre of curvature, rays retrace; a plane mirror returns normally incident rays.
Why this shows up in the exam
Autocollimation · Catadioptric instruments · Lens focal-length measurement
Learn the idea
In a lens-mirror system, light may pass through the lens twice, so every encounter must be traced in order. The lens first prepares a beam for the mirror; after reflection, the returning beam sees the lens from the opposite direction.
🧠 Memory hook: Count encounters, not components: a lens can act twice.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- 1/f_l = 1/v - 1/u — apply at each lens passage
- 1/f_m = 1/v + 1/u — apply at the mirror with its signed coordinates
How to approach it
- 1Create a coordinate diagram
- 2Process lens, mirror and return lens sequentially
- 3Apply coincidence or retracing conditions last
Common slip-ups that cost marks
- •Applying the lens only once
- •Failing to reverse propagation after the mirror
- •Adding lens and mirror powers blindly
🌟 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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