Why light bends towards the normal when it travels from rarer to denser medium. Explain with diagram.
The light propagation is described, in the simplest case, by . The quantity is called phase, and a surface on which at a given time the phase is constant, is called wave-front. The phase-velocity is the ratio of the distance between two neighbor wave-fronts of the same phase , and the time needed for the light to travel a distance equal to the distance between two neighbor wave-fronts. This time is given by
Note that the light frequency doesn't change from medium to medium, therefore doesn't change.
For illustration of the situation imagine the following scenario:
Consider a front wave of phase (red line) touching at the time the point on the separation surface between the two media, then at a time the point of the front wave touches a point of the separation surface, and at a time the point of the front wave touches the point of the separation surface. Let the points be chosen so as , and . As the velocity of the wave is smaller in ,
the distance that the wave can travel during the time is smaller,
(hence the distance between two consecutive wave-fronts is smaller.)
In consequence, the angle of the wave-front with the separation surface is smaller in than in . Finally, note that the angle between the front wave in and the separation surface is exactly equal to the refraction angle (i.e. between the normal to the separation surface and the normal to the wave-front).