write Huygen's principle of light wave . Prove the law of reflection or refraction of light on the basis of Huygen's principle of light wave.
Answers
Answer:
Huygen's principle states that every point on the wavefront may be considered a source of secondary spherical wavelets which spread out in the forward direction at the speed of light. The new wavefront is the tangential surface to all these secondary wavelets.
Reflection using Huygens Principle
We can see a ray of light is incident on this surface and another ray which is parallel to this ray is also incident on this surface. Plane AB is incident at an angle ‘ i ‘ on the reflecting surface MN. As these rays are incident from the surface, so we call it incident ray. If we draw a perpendicular from point ‘A’ to this ray of light, Point A, and point B will have a line joining them and this is called as wavefront and this wavefront is incident on the surface.
These incident wavefront is carrying two points, point A and point B, so we can say that from point B to point C light is travelling a distance. If ‘ v ‘ represents the speed of the wave in the medium and if ‘ r ‘ represents the time taken by the wavefront from the point B to C then the distance
BC = vr
In order the construct the reflected wavefront we draw a sphere of radius vr from the point A. Let CE represent the tangent plane drawn from the point C to this sphere. So,
AE = BC = vr
If we now consider the triangles EAC and BAC we will find that they are congruent and therefore, the angles ‘ i ‘ and ‘r ‘ would be equal. This is the law of reflection
Refraction using Huygen’s principle
We know that when a light travels from one transparent medium to another transparent medium its path changes. So the laws of refraction state that the angle of incidence is the angle between the incident ray and the normal and the angle of refraction is the angle between the refracted ray and the normal.
The incident ray, reflected ray and the normal, to the interface of any two given mediums all lie in the same plane. We also know that the ratio of the sine of the angle of incidence and sine of the angle of refraction is constant.
We can see a ray of light is incident on this surface and another ray which is parallel to this ray is also incident on this surface. As these rays are incident from the surface, so we call it incident ray.
Let PP’ represent the medium 1 and medium 2. The speed of the light in this medium is represented by v1 and v2. If we draw a perpendicular from point ‘A’ to this ray of light, Point A, and point B will have a line joining them and this is called as wavefront and this wavefront is incident on the surface.
If ‘ r ‘ represents the time taken by the wavefront from the point B to C then the distance,
BC = v1 r
So to determine the shape of the refracted wavefront, we draw a sphere of radius v2r from the point A in the second medium. Let CE represent a tangent plane drawn from the point C on to the sphere. Then, AE = v2r, and CE would represent the refracted wavefront. If we now consider the triangles ABC and AEC, we readily obtain
"see the pic for equation"
where’ i ‘ and ‘ r ‘ are the angles of incidence and refraction, respectively. Substituting the values of v1 and v2 in terms of we get the Snell’s Law,
n1 sin i = n2 sin r
hope it helps you
sorry for the late
