Answer
(a) $0.95KW/m^2$
(b) $1.9KW/m^2$
(c) $3.2\mu J/m^3$
(d) $1.0\times 10^{-11}N$
(e) The laser beam must be normal to the plane of the mirror.
Work Step by Step
(a) We know that
$I_{avg}=\frac{P_{avg}}{\pi r^2}$
We plug in the known values to obtain:
$I_{avg}=\frac{0.75\times 10^{-3}W}{(3.14)(0.5\times 10^{-3})^2}$
$I_{avg}=0.95KW/m^2$
(b) The peak intensity can be determined as
$I_{peak}=2I_{avg}$
We plug in the known values to obtain:
$I_{peak}=2(955W/m^2)$
$I_{peak}=1.9KW/m^2$
(c) We know that
$u_{avg}=\frac{P_{avg}}{\pi r^2c}$
We plug in the known values to obtain:
$u_{avg}=\frac{0.75\times 10^{-3}W}{(3.14)(0.5\times 10^{-3})^2(3\times 10^8m/s)}$
$u_{avg}=3.18\times 10^{-6}J/m^3=3.2\mu J/m^3$
(d) We know that
$f_{max}=\frac{2I_{peak}A}{c}$
$f_{max}=\frac{2(I_{avg})A}{c}$
$f_{max}=\frac{4P_{avg}}{c}$
We plug in the known values to obtain:
$f_{max}=\frac{4(0.75\times 10^{-3}W)}{3\times 10^8m/s}$
$f_{max}=1.00\times 10^{-11}N$
(e) We know that for the case of maximum force, the orientation of the laser beam must be normal to the plane of the mirror.
