# Huygen's Principle

Huygen's principle explain how wave theory can be used to explains the laws of geometric optics. Huygen's principle states that:

"Every point on a wave-front may be considered a source of secondary spherical wavelets which spread out in the forward direction at the speed of the wave. The new wave-front is the tangential surface to all of these secondary wavelets."

The laws of reflection and refraction can be explained using Huygens' principle.

## Problems from IIT JEE

**PARAGRAPH (IIT JEE 2007): **
The figure shows a surface XY separating two transparent media, medium-1 and medium-2. The lines ab and cd represent wavefronts of a light wave travelling in medium-1 and incident on XY. The lines ef and gh represents wavefronts of the light wave in medium-2 after refraction.

**Question 1: **
Light travels as a,

- parallel beam in each medium.
- convergent beam in each medium.
- divergent beam in each medium.
- divergent beam in one medium and convergent beam in other medium.

**Solution: **
The wavefronts in medium 1 are parallel to each other. Hence incident beam consists of parallel light rays. Same is true for refracted beam in the medium 2. Thus, A is correct.

**Question 2:**
The phases of the light wave at c, d, e and f are $\phi_c$, $\phi_d$, $\phi_e$ and $\phi_f$ respectively. It is given that $\phi_c\neq \phi_f$.}

- $\phi_c$ cannot be equal to $\phi_d$.
- $\phi_d$ can be equal to $\phi_e$.
- $(\phi_d-\phi_f)$ is equal to $(\phi_c-\phi_e)$.
- $(\phi_d-\phi_c)$ is not equal to $(\phi_f-\phi_e)$.

**Solution: **
By definition, the phase at all points on a wavefront is equal. Thus, $\phi_c=\phi_d$ and $\phi_e=\phi_f$. Hence, $(\phi_d-\phi_f)=(\phi_c-\phi_e)$. Also, since $\phi_c\neq\phi_f$, we get $(\phi_c=\phi_d)\neq (\phi_e=\phi_f)$. Thus C is correct option.

**Question 3: **
Speed of light is,

- the same in medium-1 and medium-2.
- larger in medium-1 than in medium-2.
- larger in medium-2 than in medium-1.
- different at b and d.

**Solution: **
The ray of light travels normal to the wavefront.

The ray bends towards the normal while going from medium 1 to medium 2. Hence, by Snell's law, medium 2 is denser than medium 1 i.e., $\mu_2 > \mu_1$. Thus, $v_2 = c/\mu_2 < c/\mu_1 = v_1$ i.e., speed of light is larger in medium 1. Thus B is correct choice.

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