Explain refraction of light from a denser to a rear medium, using the concept of wavefronts.

Explanation

where, `BC=v_1 tau,AD=v_2 tau,v_2 gt v_1,tau=` time taken to travel optical path by light.
AB - incident wave front
DC = refracted wave front.
i = angle of incidence in medium (1)
For `I ge i_e` , total internal reflection takes place at the interface PQ.
For `i lt i_e`, there will be refraction of light fron denser to rarer medium
From the right angled triangle ABC
`sin i=(BC)/(AC)=(v_1 tau)/(AC)" "...(1)`
and from the right angled triangle ADC,
`sin r =(AD)/(AC)=(v_2 tau)/(AC)" "...(2)`
`(1) div (2)` gives `(sin i)/(sinr) =(v_1)/(v_2)" "...(3)`
Since, `v_1 prop (1)/(n_1) and v_2 prop (1)/(n_2)`
equation (3) may be written as `(sin i)/(sin r)=(n_2)/(n_1)` where , `n_2 lt n_1`
therefore n_1 sin i=n_2 sin r`.