JEE Main & Advanced Physics Ray Optics Total Internal Reflection (TIR)

When a ray of light goes from denser to rarer medium it bends away from the normal and as the angle of incidence in denser medium increases, the angle of refraction in rarer medium also increases and at a certain angle, angle of refraction becomes \[{{90}^{o}}\], this angle of incidence is called critical angle (C).

When Angle of incidence exceeds the critical angle than light ray comes back in to the same medium after reflection from interface. This phenomenon is called Total internal reflection (TIR).

(1) \[\mu =\frac{1}{sin\,C}=cosec\,C\] where \[\mu \to \,{{\,}_{\text{Rarer}}}{{\mu }_{\text{Denser}}}\]

(2) Conditions for TIR

(i) The ray must travel from denser medium to rarer medium.

(ii) The angle of incidence i must be greater than critical angle C

(3) Dependence of critical angle

(i) Colour of light (or wavelength of light) : Critical angle depends upon wavelength as \[\lambda \propto \frac{1}{\mu }\propto \text{sin}\,C\]

(a) \[{{\lambda }_{R}}>{{\lambda }_{V}}\Rightarrow {{C}_{R}}>{{C}_{V}}\]

(b) Sin C \[=\frac{1}{_{R}{{\mu }_{D}}}=\frac{{{\mu }_{R}}}{{{\mu }_{D}}}=\frac{{{\lambda }_{D}}}{{{\lambda }_{R}}}=\frac{{{v}_{D}}}{{{v}_{R}}}\] (for two media)

(ii) Nature of the pair of media : Greater the refractive index lesser will be the critical angle.

(a) For (glass- air) pair \[\to \,\,{{C}_{\text{glass}}}={{42}^{o}}\]                                

(b) For (water-air) pair \[\to \,\,{{C}_{\text{water}}}={{49}^{o}}\]

(c) For (diamond-air) pair  \[\to \,\,{{C}_{\text{di amond}}}={{24}^{o}}\]

(iii) Temperature : With temperature rise refractive index of the material decreases therefore critical angle increases.