Rays in Spheres, Drops and Bubbles
At each spherical boundary, apply Snell's law using the radius through the incidence point as normal; subsequent incidence angles follow from the internal triangle.
Why this shows up in the exam
Glass beads · Water drops · Air bubbles in transparent media
Learn the idea
Curved transparent boundaries change the local normal, so refraction and total reflection must be checked at each point. On a sphere the normal is always a radius, turning a complicated boundary into a sequence of triangles.
🧠 Memory hook: On a sphere, draw the radius first: it is the normal.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- n1 sin(i) = n2 sin(r) — local refraction at a spherical boundary
- sin(C) = n2/n1 — local TIR threshold when travelling denser to rarer
How to approach it
- 1Join incidence point to the centre
- 2Apply Snell's law locally
- 3Use the internal triangle before the next surface
Common slip-ups that cost marks
- •Using the principal axis as the normal everywhere
- •Applying one incidence angle at both surfaces
- •Treating a bubble index as greater than its liquid
🌟 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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