A ray of light in air strikes a glass surface. Is there a range of angles for which total internal reflection occurs? Explain.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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When a ray of light from material A with a refractive index Na enters into material B with a refractive index Nb, the relation between the angle of incidence Ac and the angle of refraction Ar is given by Snell's Law as sin Ac / sin Ar = Nb / Na.

The critical angle is the minimum angle of incidence at which total internal reflection takes place. At this angle Ar = 90 degrees and sin Ar = 1, which gives sin Ac = (Nb/Na). The angle Ac is equal to arc sin (Nb/Na).

Now in the case of a ray of light traveling from air and striking a glass surface, the ratio of the refractive index of glass and the refractive index of air is greater than 1. So the value of arc sin(Nb/Na) is not defined.

Therefore total internal reflection cannot take place in this case.

A ray of light moving from air to glass is always refracted into glass, irrespective of the angle of incidence.

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