Question

proof of angle of incidence = angle of reflection

Answer 1

hay there ..

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first u know.

Reflection the angle of incidence always to b equal...angle of reflection

ok we will proof it by simple mathematical example.

lets see

angel of incidence equal angel of reflection
Let a right ray AO from a source A strike a plane mirror at O and reflected as ray OB. Let B be a point on ray OB and let ON be the normal to the mirror at O. The angle of incidence is ‘x’ and angle of reflection is ‘y’, as shown. Let ‘t’ be the time taken for the ray to travel the distance AO + OB and ‘c’ be the velocity of light, which is a constant.

The time ‘t’ can be worked out
t = C/AO + C/OB

t= c[1/√a2 + p2 + 1/ /√(l-a)2 + q2 ]

Therefore, the derivative dt/da must be 0.

0 = [a/√a2 + p2 = (l-a) /√(l-a)2 + q2 ]

[1/√a2 + p2 =√(l-a)2 + q2 ]

But as per trigonometry, this is same as sin(x) = sin(y) or x = y.
Hence,
The Angle of Incidence = Angle of Reflection

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@Srk6

Answer 2

The time ‘t’ can be worked out
t = C/AO + C/OB

t= c[1/√a2 + p2 + 1/ /√(l-a)2 + q2 ]

Therefore, the derivative dt/da must be 0.

0 = [a/√a2 + p2 = (l-a) /√(l-a)2 + q2 ]

[1/√a2 + p2 =√(l-a)2 + q2 ]

But as per trigonometry, this is same as sin(x) = sin(y) or x = y.
Hence, The Angle of Incidence = Angle of Reflection
Therefore it proved