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When a ray of light travels from an optically denser medium to a rarer medium, the refracted ray is bent away from the normal e.g the incident ray ‘AO1’ is partially reflected (O1C) and partially refracted (O1B), the angle of refraction being larger than the angle of incidence. As the angle of incidence increases, the angle of refraction also increases, till for the ray (AO3), the angle of refraction is 90° i. e Ðr = 90°. The refracted ray is bent so much away from the normal that it passes along the boundary of the two media, i.e along AO3D.

If the angle of incidence is increased still further (e.g ray AO4) refraction is not possible and the incident ray is totally reflected, called total internal reflection.

“When a ray of light enters from an optically denser medium into an optically rarer medium and is incident at an angle greater than critical angle, the ray is totally reflected back into the same medium called “total internal reflection”.

Critical angle: “The angle of incidence (iC) at which total internal reflection just occurs \left( {i.e\,\angle r\, = \,90^\circ } \right)and the refracted ray pass along the boundary of the two media”.

Relation between critical angle and refractive index:

From Snell’s law, glass–air interface

\frac{{\sin \,i}}{{\sin \,r}}\, = \,\frac{1}{{{n_{ga}}}}

At i\, = \,{i_c},\,\,r\, = \,90^\circ

\begin{array}{l} \therefore \,\,\,\,\,\frac{{\sin \,{i_C}}}{{\sin \,90^\circ }}\, = \,\frac{1}{{{n_{ga}}}}\\ \,\,\,\,\,\,\,\sin \,{i_C}\, = \,\frac{1}{{{n_{ga}}}} \end{array}


n\, = \,\frac{1}{{\sin \,{i_C}}}


NOTE: Critical angle for some transparent media.

Substance Refractive index Critical angle
Water 1.33 48.75°
Crown glass 1.52 41.14°
Dense flint glass 1.65 37.31°
diamond 2.42 24.41°

Necessary conditions for total internal reflections:

(a) Light must travel from an optically denser medium to a rarer medium.

(b) The angle of incidence should be greater than critical angle for the given pairs of media.