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Question : 26
Total: 35
SECTION - C
(a) A plane wave-front propagating in a medium of refractive index '
Use Huygen's construction of secondary wavelets to trace the retracted wave-front. Hence, verify Snell's law of refraction.
OR
(b) Using Huygen's construction, show how a plane wave is reflected from a surface. Hence, verify the law of reflection.
Solution: 👈: Video Solution
(a) A plane wavefront AC is incident on the plane of separation XY of two media of refractive indices µ 1 and µ 2 ( µ 2 > µ 1 ) making an angle i . This is known as angle of incidence.
When the wavefront touches the pointA , the point becomes a source of secondary wavelets. Thus, when the whole waveform passes through the X Y plane, each point of AF becomes the source of secondary wavelets.
When pointC of the wavefront in medium 1 traverses CF distance by that time ( t ) the wavelet from point A traverses AD distance. If v 1 and v 2 are the speeds of light in medium 1 and 2 respectively, then A D = v 2 t and C F = v 1 t .
Refracted wavefront DF which is obtained by drawing a tangent to the arc having radiusv 2 t and centre A . The angle made by the tangent with the plane XY is r . This is known as angle of refraction.
The perpendiculars drawn on wavefrontAC are the incident rays. The perpendiculars drawn on wavefront D F are the refracted rays.
AN and TF are the perpendiculars drawn on XY , the plane of separation of the two media.
∠ C A F = ∠ i = 90 ∘ − ∠ N A C = 90 ∘ − ( 90 ∘ − ∠ S A N )
∴ ∠ S A N = ∠ i
Similarly, ∠ Q F T = ∠ r
In △ A C F ,
s i n i =
=
In△ ADF ,
s i n r =
=
∴
=
=
= 1 µ 2
This is Snell's law.
OR
(b) A plane wavefrontAC is incident on a plane reflector XY making an angle i . This is known as angle of incidence.
Each and every point of the wavefront when touches the reflector becomes a source of secondary wavelets. When the wavefront touches the pointA , the point becomes a source of secondary wavelets. Thus, when the whole waveform touches the XY plane, each point of AF becomes the source of secondary wavelets. When point C of the wavefront in medium 1 traverses CF distance by that time ( t ) the wavelet from point A traverses AD distance. If v 1 is the speeds of light in medium then A D = v 1 t and C F = v 1 t .
Reflected wavefront DF which is obtained by drawing a tangent to the arc having radiusv 1 t and centre A . The angle made by the tangent with the plane XY is r . This is known as angle of refraction.
The perpendiculars drawn on wavefrontA C are the incident rays. The perpendiculars drawn on wavefront DF are the reflected rays.
AN and TF are the perpendiculars drawn on XY , the plane reflector.
∠ C A F = ∠ i = 90 ∘ − ∠ N A C
= 90 ∘ − ( 90 ∘ − ∠ S A N )
∴ ∠ S A N = ∠ i
Similarly, ∠ Q F T = ∠ r
In△ ACF and △ AFD
∠ A C F = ∠ A D F = 90 ∘
C F = A D
AF is the common side
So, the triangles are congruent.
∴ ∠ C A F = ∠ A F D
∴ i = ∠ r
This is law of reflection.
When the wavefront touches the point
When point
Refracted wavefront DF which is obtained by drawing a tangent to the arc having radius
The perpendiculars drawn on wavefront
In
This is Snell's law.
OR
(b) A plane wavefront
Each and every point of the wavefront when touches the reflector becomes a source of secondary wavelets. When the wavefront touches the point
Reflected wavefront DF which is obtained by drawing a tangent to the arc having radius
The perpendiculars drawn on wavefront
In
So, the triangles are congruent.
This is law of reflection.
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