Grade 10 Science · The Critical Angle
The angle of no escape
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The angle of no escape

Light leaving water for air bends AWAY from the normal — the exit angle is always wider than the angle inside. Tilt the ray steeper and steeper and the escaping ray flattens toward the surface… until, at one particular angle, it cannot leave at all. Past the critical angle the surface behaves like a perfect mirror: total internal reflection. The formula is Snell's law pushed to its limit (θ2=90°\theta_2 = 90°): sinθc=n2n1\sin\theta_c = \dfrac{n_2}{n_1} — read aloud: sine theta-c equals n-two over n-one. Same subscript convention as Snell's law: n1n_1 is the index of the medium the light is trying to LEAVE — the slower one it started in — and n2n_2 the index of the faster medium beyond the surface. θc\theta_c, said theta-c, is the critical angle in degrees, and it is what you are solving for.

One direction only: this trap needs light heading from the slower medium toward the faster one — from glass toward air, never air toward glass; going the other way, light always gets in. And it is no curiosity: an optical fibre is a thread of glass whose light strikes the wall past the critical angle millions of times in a row — the internet arrives at your house by trapped light.