Critical Angle
For n1 > n2, sin(C) = n2/n1. The critical angle is defined only for incidence from the optically denser to the rarer medium.
Why this shows up in the exam
Gemstone brilliance · Prism design · Escape-cone calculations
Learn the idea
The critical angle is the denser-side incidence angle whose refracted ray just grazes the boundary. As incidence increases from a higher-index medium, the refracted ray moves toward the surface until its angle reaches 90 degrees.
🧠 Memory hook: Critical means the refracted ray is at 90 degrees.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sin(C) = n2/n1 — critical angle for light travelling from n1 to n2 with n1 > n2
How to approach it
- 1Identify the incident denser medium
- 2Set r = 90 degrees in Snell's law
- 3Compare the actual incidence with C
Common slip-ups that cost marks
- •Using the rarer-to-denser direction
- •Writing n1/n2 instead of n2/n1
- •Calling every grazing ray total internal reflection
🌟 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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