Layered Media and Optical Path
For normal incidence, optical path length is sum(n_j t_j), while paraxial apparent thickness viewed from index n0 is sum(n0 t_j/n_j).
Why this shows up in the exam
Multilayer windows · Liquid-level metrology · Optical delay plates
Learn the idea
Each transparent layer contributes its own refraction, apparent thickness and optical path. A stack is handled layer by layer; a thick high-index layer does not behave like the same physical thickness of air.
🧠 Memory hook: For layers, add optical contributions, not bare thicknesses.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- OPL = sum(n_j t_j) — normal optical path through plane layers
- d_app = sum(n0 t_j/n_j) — paraxial apparent thickness seen from medium n0
How to approach it
- 1List layer thickness and index
- 2Choose optical path or apparent-depth relation
- 3Add layer contributions before solving
Common slip-ups that cost marks
- •Averaging refractive indices arithmetically
- •Treating all layers as one interface
- •Mixing optical path with apparent depth
🌟 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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