A small laser emits light at a power of 5.00 mW. The laser beam is focussed unti

Question

A small laser   emits   light   at   a power of 5.00 mW. The laser beam is focussed until its diameter  
matches the 1266 nm diameter of a sphere placed in its path. The sphere is perfectly absorbing  
and has a density of 5.00 x103 kg/m3.

a. Calculate   the   average   energy   per   unit   time   per   unit   area   (S).
b. Find   the   maximum   values   of   E   and   B.
c. Calculate   the   radiation   pressure   on   the   sphere   and   the   force   exerted   on   the   sphere.
d. Find   the   acceleration   of   the   sphere.

Explanation / Answer

a)

I = P/pid^2/4 = 5.00*10^-3/pi*2.00*633*10^-9/4 = 3.97*10^9w/m^2

b) the radiation pressure is

Pr = I/C = 3.97*10^9w/m^2/2.998*10^8m/s = 13.2pa

c)

Fr pid^2/4 Pr = P* pr/I = 5.00*10^-3*13.2Pa/3.97*10^9 = 1.67*10^-11N

d)   

the accel

a = Fr / m = Fr / roh (pid^3/6) = 6*(1.67*10^-11)/pi*(5.00*10^3)*((2.00)*(633*10^-9)) = 3.14*10^3m/s^2

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