Define critical angle. Obtain a relation between the refractive index and critical angle for a pair of media. Does critical angle depend on the colour of light ? Explain.

Explanation

For definition, see Point Number 25 under the heading "Chapter At A Glance". Let as shown in Fig. 9.36, `i_c` be the critical angle in an optically denser Rarer medium medium number 1 for which angle of refraction in rarer medium number 2 is 90°. Then, from Snell.s law, we have
`(sini_( c))/(sin 90^(@)) = n_(21) = 1/n_(12)`
But, `sin 90^(@)=1`, hence, `sin i_(c ) = n_(21) = 1/n_(12) =n_(2)/n_(1) ( or sin i_( c) = n_(rd) = 1/n_(dr)`)

Yes, critical angle depends on the colour of light. We know that refractive index is least for red coloured light and maximum for violet colour light. As a result critical angle for a given pair of media is least for violet colour and has a maximum value for red colour.