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I have to make a demonstration I need help pls
There are several cases where the incident ray has as its point of departure a focus of hyperbole
angle of incidence = angle of reflection
the incidence point(A)=(m,n)
The normal vector (v2) has (b(square)m;-a(square)n)
The question: make a demonstration on the trajectory of the ray reflected by a hyperbolic mirror when the incident ray starts from a focus
PS: sorry if their is mistakes i had the broblem in frensh and i don't lean maths in english
it's urgent I need an answer as soon as possible
thank you!
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the angles α and β between the tangent line and the straight lines drawn from the hyperbola foci to the given point are congruent:
Recall the physical law of reflection: the angle of incidence is equal to the angle of reflection measured from the normal. It is consistent with the geometric optical
properties above.
The reflected ray R u can be written in parametric form as shown in Equation 1 above, where v = v ( u ) is its direction. We can write q = ξu , for some positive number ξ . Since q − c 2 = r 2 , and c − o = dw , ξ must be the smallest positive real root of the quadratic equation Note that, if α is the angle formed by the vectors u and w , the maximum angle α MAX is achieved when the incident and reflected rays are tangent to the sphere, in which case.
Recall the physical law of reflection: the angle of incidence is equal to the angle of reflection measured from the normal. It is consistent with the geometric optical
properties above.
The reflected ray R u can be written in parametric form as shown in Equation 1 above, where v = v ( u ) is its direction. We can write q = ξu , for some positive number ξ . Since q − c 2 = r 2 , and c − o = dw , ξ must be the smallest positive real root of the quadratic equation Note that, if α is the angle formed by the vectors u and w , the maximum angle α MAX is achieved when the incident and reflected rays are tangent to the sphere, in which case.
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