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