How to Work out the Critical Angle of a Substance

Make sure you know the Snell's Law. The general form of Snell's Law is nxsinθx=nvacuumsinθvacuum, where n is the refractive index and θ is the angle of incidence or refraction.

Find out the refractive index of the substance (or nx).

You can now do the substitution. Let's say you are using glass with a refractive index of 1.50. Therefore, the critical angle is the angle which, when it is the angle of incidence, produces an emergent ray of 90°. nglasssinθglass=nvacuumsinθvacuumWork out the Critical Angle of a Substance Step 3Bullet1.jpg 1.50sinθglass=1sin90°Work out the Critical Angle of a Substance Step 3Bullet2.jpg sinθglass=2/3Work out the Critical Angle of a Substance Step 3Bullet3.jpg θglass=41.8° (correct to 3 significant figures)

The critical angle is therefore 41.8°.