A point source of radiation power P is placed on the axis of an ideal plane mirror. The distance between the source and the mirror is n times the radius of the mirror. The force that light exerts on t

Question

A point source of radiation power P is placed on the axis of an ideal plane mirror. The distance between the source and the mirror is n times the radius of the mirror. The force that light exerts on the mirror is xc ( n 2 + y ) P ​ find x + y ?

TestHub · Accepted Answer

Source at height h = n R Intensity at distance r from the source: 4 π r 2 P ​ Force: F = ∫ c 2 ​ 4 π r 2 P ​ cos 2 θ d A Ring element: d A = 2 π ρ d ρ F = c P h 2 ​ ∫ 0 R ​ ( h 2 + ρ 2 ) 2 ρ d ρ ​ = 2 c P ​ h 2 + R 2 R 2 ​ F = 2 c ( n 2 + 1 ) P ​ x = 2 , y = 1 , so x + y = 3

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