Question

What is Huygens’ wave theory? Enunciate Snell’s law of refraction of light by using this theory.

Hint:

Huygens’ principle explains reflection, refraction, diffraction, but not polarization.

Answer 1

Step 1: Statement of Huygens’ principle.
Every point on a wavefront is a source of secondary wavelets, which spread out in all directions with speed of light in that medium. The new wavefront is the envelope of all secondary wavelets.
Step 2: Application to refraction.
Consider a plane wavefront incident on a refracting surface separating two media: - Speed in medium 1: $v_1$, refractive index $n_1$. - Speed in medium 2: $v_2$, refractive index $n_2$.
Step 3: Geometry of refraction.
From Huygens’ construction: \[ \frac{\sin i}{\sin r} = \frac{v_1}{v_2}. \]
Step 4: Use relation between speed and refractive index.
Since $v \propto \tfrac{1}{n}$, \[ \frac{\sin i}{\sin r} = \frac{n_2}{n_1}. \]
Step 5: Conclusion.
This is Snell’s law of refraction, derived from Huygens’ wave theory.