06M.3 Suppose we prepare a beam of photons with wave- length λ and intensity I whose...
06M.3 Suppose we prepare a beam of photons with wave- length λ and intensity I whose spin angular momentum vectors are aligned with their direction of motion, and we allow these photons to fall on a circular metal plate of mass M and radius R that is free to rotate around an axis per- pendicular to the plate and parallel to the beam of light. As the photons are absorbed by the metal plate, the plate will have to rotate to conserve angular momentum. (a) Find a formula for the time T the beam has to shine on the plate to get it rotating at a certain final angular speed . (b) Find the numerical value of T if M = 50 g, R-3 cm, I 1000 W/m2 (the intensity of sunlight), the light is in the visible range with an average wavelengthA 550nm, and we want a final rotation rate of 1 turn/s. Comment on why the Beth experiment mentioned in the chapter is so difficult. (c) Suppose we can prepare a beam of microwave pho- tons with the same intensity I but 0.55 cm. If we allowed this beam to fall on the same metal plate, would T increase or decrease compared to the answer in part (b)? Explain your result physically (not simply by appealing to the equation you found for the first part). By what factor will T change?