What is Critical angle and total internal reflection? — Physics

Definition 3.16 High School Physics · Chapter 3 — Refraction of Light

Let light travel in a medium of index $n_1$ toward a medium of smaller index $n_2 < n_1$ . The critical angle $i_c$ is the angle of incidence for which the refracted ray grazes the surface ( $i_2 = 90^\circ$ ). For $i_1 > i_c$ no refracted ray exists: the surface reflects all the light back into the first medium, following the law of reflection. This is total internal reflection.

From water toward air, at increasing incidence: refraction away from the normal, then a refracted ray grazing the surface at the critical angle, then total internal reflection — the surface has become a perfect mirror.

Examples

Example 3.18 (Three critical angles)

Toward air: for water, $\sin i_c = 1/1.33 = 0.752$ , so $i_c = 48.8^\circ$ ; for glass, $\sin i_c = 1/1.50$ , so $i_c = 41.8^\circ$ ; for diamond, $\sin i_c = 1/2.42 = 0.413$ , so $i_c = 24.4^\circ$ . The higher the index, the narrower the escape cone: in diamond, any ray more than $24.4^\circ$ off a facet’s normal is trapped — the secret of its sparkle, dissected in Problem 3.1.

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Examples

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