Question

A laser emits light at power 5.49 mW and wavelength 633 nm. The laser beam is focused (narrowed) until its diameter matches the 1230 nm diameter of a sphere placed in its path. The sphere is perfectly absorbing and has density 5.00 × 103 kg/m3. What are (a) the beam intensity at the sphere's location, (b) the radiation pressure on the sphere, (c) the magnitude of the corresponding force, and (d) the magnitude of the acceleration that force alone would give the sphere?

Answer 1

radius of beam R = d/2 = 1230/2 nm = 6150 nm

Intensity = power/area of cross section = power/(pi*R^2)

I = 5.49*10^-3/(pi*(6150*10^-9)^2)

I = 46203219.65 W/m^2

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radiation pressure P = I/c = 46203219.65/(3*10^8) = 0.154 Pa

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force = pressure *area of sphere/2 = P*4*pi*R^2/2 = P*2*pi*R^2

force = 0.154*2*pi*(6150*10^-9)^2

Force F = 3.65*10^-11 N

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acceleration a = F/m

m = mass = density*volume = D*(4/3)*pi*R^3

acceleration = 3.65*10^-11/(5*10^3*(4/3)*pi*(6150*10^-9)^3) = 7.49 m/s^2