Fermat's Principle: Proving Law of Reflection

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Fermat's principle asserts that light travels along the path that minimizes or maximizes travel time between two points. The discussion focuses on demonstrating that a light ray reflecting off a surface follows the law of reflection, which states that the angle of incidence equals the angle of reflection. A proposed solution suggests using triangle symmetry to prove this concept without excessive mathematical complexity. A reference link is provided for further exploration of the proof. The conclusion emphasizes that the law of reflection is a direct consequence of Fermat's principle.
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Homework Statement


Fermat’s principle states that the path of a light ray between two points is such that the time to traverse that path is an extremum (either a minimum or a maximum) when compared with the times for nearby paths. Consider two points A and B on the same side of a reflecting surface, and show that a light ray traveling from A to B via a point on the reflecting surface will take the least time if its path obeys the law of reflection. Thus, the law of reflection follows from Fermat’s principle.

Homework Equations



Triangle symmetry

The Attempt at a Solution


would this be a reasonable proof without involving to much maths? http://www.math.uiowa.edu/~stroyan/CTLC3rdEd/ProjectsOldCD/estroyan/cd/27/index.htm
 
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looks a good enough way to prove it.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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