XY is a plane surface separating a denser medium of refractive index from a rarer medium. If c1 and c2 are the velocities of light in rarer medium and denser medium then,
1m2 represents refractive index of medium 2 with respect to 1.
Let AB be the incident plane wavefront. Let the wavelet B strike XY at A
| in t seconds.
In the same time t seconds, A travels in the denser medium with velocity c
2 and covers a distance AB
|= c
2t. With A as centre and c
2t as radius, draw an arc as shown. Repeat for points P and so on. The tangent to these arcs gives the reflected wavefront A
|B
|. One can prove that A
|B
| is the true refracted wave front by proving,
BA
|= BN + NA
|= DP + NA
|
If one has to prove A
|B
| is the true wave front then it is sufficient to prove that
or
and
All the incident, normal and refracted rays lie in the same plane.
