Escape Cone and Visibility Through a Surface
For a point at depth h in higher-index medium, the escape-cone half-angle is C and the surface-circle radius is h tan C for a plane boundary.
Why this shows up in the exam
Underwater viewing · Submerged-light design · Aquarium illumination
Learn the idea
Only rays inside an interface's escape cone can leave a higher-index medium. A submerged observer sees the outside world compressed into a cone, while an underwater source illuminates only a finite patch above.
🧠 Memory hook: The critical angle is the rim of the escape window.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sin(C) = n_out/n_in — escape-cone half-angle
- radius = h tan(C) — circular patch at a plane surface
How to approach it
- 1Locate the source or observer
- 2Draw the limiting ray at C
- 3Use right-triangle geometry at the surface
Common slip-ups that cost marks
- •Using the full cone angle as C
- •Using apparent depth in the geometric radius
- •Forgetting which side contains the source
🌟 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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