In the figure, a laser beam of power 4.04 W and diameter 2.60 mm is directed upw

Question

In the figure, a laser beam of power 4.04 W and diameter 2.60 mm is directed upward at one circular face (of diameter d < 2.60 mm) of a perfectly reflecting cylinder. The cylinder is levitated because the upward radiation force matches the downward gravitational force. If the cylinder's density is 1.79 g/cm3, what is its height H in millimeters?

http://edugen.wileyplus.com/edugen/courses/crs4957/art/qb/qu/c33/fig33_39.gif

Explanation / Answer

Power, P = 4.04 W, D = 2.6mm = 0.0026m

density = 1.79g/cc = 1.79*10^3kg/m^3

F = mg

2P/c = d*pi*(D^2/4)*H*g

H = 2P/(d*g*c*pi*D^2/4) = 2*4.04/(1.79*10^3*9.8*3*10^8*3.142*0.0026^2/4) = 2.89*10^-7m = 2.89*10^-4mm

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