Using Huygen's principle construct a refracted wavefront when a plane wavefront is incident on plane surface from an optically denser meidum side. Using this figure, obtain the condition of critical angle and total internal reflection.

Explanation

When a plane wavefront AB travelling in an optically denser medium of refractive index `n_(1)` with a speed `c_(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)ltn_(1)`) with a speed `c_(2)` (where `c_(2)gtc_(1)`). Thus, a refracted wavefront CD is formed as shown in figure. As `c_(2) gt c_(1)`, hence obviously the angle of refraction is greater than the angle of incidence (i.e., `rgti`). However, Snell.s law holds good, according to which
`(sini)/(sinr)=(n_(2))/(n_(1))=(c_(1))/(c_(2))`
Condition for 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^(@)`, then
`(sini_(c))/(sin90^(@))=(n_(2))/(n_(1))=(c_(2))/(c_(1)) or sini_(c)=(n_(2))/(n_(1))=(c_(1))/(c_(2))=(1)/(n_(12))`
This angle `i_(c)` is called the critical angle.
Condition for total internal reflection: If angle of incidence `igti_(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.