A wave satisfying eq passes from one medium in which the phase velocity for all wavelengths is v 1 to another medium in which the phase velocity is v 2 The incident wave gives rise to a reflected wave that returns to the original medium and a refracted wave that changes direction as it passes throu...

Let k i i and A i i 1 2 3 be the wave number frequency and amplitude of the incident refracted and ...

A wave satisfying ? eq. passes from one medium in which the phase velocity for all wavelengths

Question:

A wave satisfying?eq.

passes from one medium in which the phase velocity for all wavelengths is v₁ to another medium in which the phase velocity is v₂. The incident wave gives rise to a reflected wave that returns to the original medium and a refracted wave that changes direction as it passes through the interface. Suppose that the interface is the plane z = 0 and the incoming wave is propagating in a direction at an angle ?₁ to the normal z?. Prove the law of specular reflection, which states that the reflected wave propagates at an angle ? ? ?₁ with respect to the normal z?. Also prove Snell?s law, which states that the wave in the second medium propagates at an angle ?₂ from the normal z?, where sin ?₂/ sin ?1 = v₂/v₁. Use the fact that the wave must be continuous across the interface at z = 0.