Law of reflection by Fermat’s principle | Optics

Law of reflection by Fermat’s principle

Fermat's principle

• According to Fermat’s principle of extremum path, a ray of light in passing from one point to another through a set of media by any number of reflections or refractions selects a path for which the time taken is either minimum or maximum.

Law of reflection by Fermat's principle

• Since whole path is travelled by light in air.
• So, the optical path between A and B is
• l = AO + OB
• l = √{a² + x²} + √{b² + (c - x)²)}
• From Fermat’s principle, the position of point O is such the optical path l should be either maximum or minimum.
• dl/dx = 0
• Therefore

• ∴ sin i = sin r
• or ∠ i = ∠ r

Conclusion

• Since  i  is angle of incidence and  r  is angle of reflection
• So, for reflection form any surface, the angle of incidence should be equal to the angle of reflection.
• The incident ray, reflected ray and normal to the reflecting surface all should lie in the same plane and that plane is plane of incidence.

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