You are given a parabolic mirror whose inner surface is silvered. The equation of the curve formed by its intersection with x − y plane is given by y = x 2 /4 . A ray travelling in x − y plane along l

Question

You are given a parabolic mirror whose inner surface is silvered. The equation of the curve formed by its intersection with x − y plane is given by y = x 2 /4 . A ray travelling in x − y plane along line y = x + 3 hits the mirror in second quadrant and gets reflected. The unit vector in the direction of reflected ray is :-

TestHub · Accepted Answer

Point of intersection of two curves, y = 4 x 2 ​ and y = x + 3 is, (-2, 1) dx dy ​ = 2 x ​ i.e., ( dx dy ​ ) x = − 2 ​ = 2 − 2 ​ = − 1 tan β = slope of incident ray RP = 1 or β = 4 5 ∘ and tan α = ​ ( dx dy ​ ) x = − 2 ​ ​ = 1 ⇒ α = 4 5 ∘ From geometry we can show that ∠ i = ∠ r = 0 ∘ i.e., the ray is incident normally. Hence, the desired unit vector : A = 2 ​ 1 ​ ( − i ^ − j ^ ​ )

Physics - Geometrical Optics Question with Solution | TestHub

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