The discussion centers on calculating the rotation rate of a reflected beam of light from a rotating plane mirror. When the mirror rotates at 100 rpm, the reflected beam rotates at 200 rpm due to the relationship between the incident angle and the reflected angle. The relevant equation discussed is 2θ = 2 dθ/dt, although it was noted that this equation is incorrect. The conclusion is that the instantaneous angular velocity of the reflected beam is double that of the mirror's rotation rate.
PREREQUISITESPhysics students, optical engineers, and anyone interested in the dynamics of light reflection and rotation mechanics.
Firstly, describe the reflected anglehidemi said:Homework Statement:: A plane mirror is in a vertical plane and is rotating about a vertical axis at 100 rpm. A horizontal beam of light is incident on the mirror. The reflected beam will rotate at:
The answer is 200 rpm.
Relevant Equations:: 2θ = 2 dθ/dt
If we know the change of angle is twice the incident angle, then the rate of rotation is 2*100 rpm = 200 rpm. Is there a better explanation of it?
I got it. Thanks!collinsmark said:Firstly, describe the reflected anglewith respect toas a function of the angle of the plane.
Secondly, take the derivative.
[Edit: also, your "2θ = 2 dθ/dt" equation is incorrect.]