# How is 2nd law of reflection applicable with congruence in maths?

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The figure is below.

Let the incoming ray of light coming from the left side and reflecting on a horizontal surface. The wave front of the incoming light ray is the geometrical place of all the points in a ray that oscillate with the same phase. This wave front is thus perpendicular to the direction of propagation.

The incoming wave front is `|AB|` . Because in the figure (as the second law of reflection states)

`/_i =/_r`

and the angles:

`/_A A'B'` and `/_r` have perpendicular sides

`/_BA A'` and `/_i` have perpendicular sides

it means `/_A A' B' -=/_BA A'`

Also from the same considerations we have

`/_B'A A' -=/_BA' A`

Thus because also

`/_AB'A' = /_A'BA =90 deg`

the triangles `AB'A'-=A'BA rArr |A'B'|-=|AB|`

**Thus the second law of reflection means in mathematical terms that the reflected front wave is congruent with the incoming front wave.**

**Sources:**