Derive the laws of reflection of light using Huygens’ principle.
Answers
Answer:
The arrow AE shows the direction of propagation of the reflected wave. ∴ Δ ABC and Δ AEC are congruent. Thus, the angle of incidence is equal to the angle of reflection. ... Thus, the laws of reflection of light can be deduced by Huygens' construction of a plane wavefront.
Answer:
☆ Huygen's principle:
‐ Each point of the wavefront is the source of a secondary disturbance and the wavelets emitting from these points spread out in all directions with the same same speed of wave.
- These wavelets emitting from the wavefront are usually referred to as secondary wavelets..and if we draw a common tangent to all other spheres, we obtain the new position of the wavefront at a later time.
(see the attachment for spherical wavefronts).
》Huygen argued that the amplitude of the secondary wavelets is maximum in forward direction and zero in the backward direction
》we can use Huygen's principle to determining the shape of wave front for a plane wave propagating through a medium.
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☆ lets derive it:
○○First see the attachment for figure!
1. plane wave AB is incident at an angle i on a reflecting surface.
2. t = time taken by wavefront to advance from point B to C , v = speed of the wave.
3. then the distance BC = vt
4. draw a sphere of radius vt from the point A in order to construct the wavefront.
5. CE represents the tangent plane drawn from point C to this sphere...so by congruent triangle..
● AE = BC = vt
6. as the triangle EAC and BAC are congruent, angle i and angle r would be equal.
This is the law of reflection.
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☆Note:
- from the above, it clears that the total time taken from a point on the object to the corresponding point on the image is same measured along the ray.
hope it helps!
