Reflection On a Plane Mirror:
Consider the light rays 1, 2 and 3 shown by solid lines. The wave fronts which are perpendicular to these light rays are shown by the thin lines. The secondary wave fronts generated are the circular fronts described.
At point a, a wave front is generated due to the secondary source on ray 2. At the same time, other wave fronts are generated at points c and b. Since wave fronts at points a and b are generated at the same time a c = c b. Thus the triangle a c b is isosceles and the angles θ1 = θ2.
Note that θ1 is the angle of incidence and θ2 is the angle of reflection.
Thus, angle of incidence = angle of reflection
Refraction of a Wave Front:
Consider the light rays 1, 2 and 3 shown by solid lines refracted to rays 1’, 2 and 3’ respectively. The wave fronts which are perpendicular to these light rays are shown by the thin lines. Consider the wave fronts to be one wavelength apart in their respective media where refractive indices n1 < n2. The incident angle is θ1 and the refracted angle is θ2. Consider the wave front at c, the front is bent in the new medium because the speed of light is slower. However, since the frequency of the waves are a constant, the wavelengths change across media to accommodate the change in speed.
Also from figure the side ac is common to the triangles abc and adc,
But the line segments ac and ad represent the wavelengths in their respective media,
Where, c is the speed of light in vacuum.
Thus, the Huygens principle can be used to prove the law of refraction. A similar exercise can be conducted for n1 > n2.
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