**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 **θ _{1 }= **

**θ**.

_{2}Note that θ_{1} is the angle of incidence and θ_{2} 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 n_{1 }< n_{2}. The incident angle is θ_{1 }and the refracted angle is θ_{2}. 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.

i.e.,

\(ϑ_1\)

\({v_1}{λ_1}\)

Also from figure the side ac is common to the triangles **abc **and **adc**,

\(ac\)

\(\frac{bc}{sinθ_1}\)

But the line segments **ac** and **ad** represent the wavelengths in their respective media,

\(\frac{λ_1}{sinθ_1}\)

\(\frac{v_1}{sinθ_1}\)

\(\frac{sin~ θ_1}{sin~θ_2}\)

\(\frac{sin~θ_1}{sin~θ_2}\)

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 n_{1 }> n_{2}.

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