• # question_answer Construct a refracted wavefront using Huygens' principle, when a plane wavefront is incidented on a plane surface from an optically denser medium, further define critical angle and obtain the condition for total internal reflection.

When a plane wavefront PQ travelling in an optically denser medium of refractive index ${{n}_{1}}$ with a speed ${{v}_{1}}$ is incident on the surface of a rarer medium at an angle of incidence, i, then the wavelets spread in the rarer medium of refractive index, ${{n}_{2}}$ (where, ${{n}_{2}}<{{n}_{1}}$) with a speed, ${{v}_{2}}$(where ${{v}_{2}}>{{v}_{1}}$). Thus, a refracted wavefront RS is formed as shown in the figure. The refracted wavefront subtends an angle of refraction, r. As ${{v}_{2}}>{{v}_{1}},$ hence, the angle of refraction is greater than the angle of incidence (i.e. r > i). However, Snell's law holds good, according to which             $\sin i/\sin r={{n}_{2}}/{{n}_{1}}={{v}_{1}}{{v}_{2}}$ Critical angle As angle i increases, value of angle r also increases. If for a certain value of $i={{i}_{c}},$ the angle of refraction just becomes$90{}^\circ ,$ then             $\frac{\sin \,{{i}_{c}}}{\sin 90{}^\circ }=\frac{{{n}_{2}}}{{{n}_{1}}}=\frac{{{v}_{1}}}{{{v}_{2}}}$ or         $\sin {{i}_{c}}=\frac{{{n}_{2}}}{{{n}_{1}}}=\frac{{{v}_{1}}}{{{v}_{2}}}$ This angle ${{i}_{c}}$ is called the critical angle. Condition for total internal reflection If angle of incidence $i>{{i}_{c}},$ then it is not possible to find refracted wavefront. In such a case, no refraction takes place and whole wavefront is totally reflected back into the denser medium. It is known as the phenomenon of total internal reflection.