A radiation of 200 W is incident on a surface which is 60 %...

A radiation of $200 \mathrm{~W}$ is incident on a surface which is $60 \%$ reflecting and $40 \%$ absorbing. The total force on the surface is (a) $107 \times 10^{-6} \mathrm{~N}$ (b) $13 \times 10^{-6} \mathrm{~N}$ (c) $107 \times 10^{-7} \mathrm{~N}$ (d) $103 \times 10^{-7} \mathrm{~N}$

A radiation of $200 \mathrm{~W}$ is incident on a surface which is $60 \%$ reflecting and $40 \%$ absorbing. The total force on the surface is
(a) $107 \times 10^{-6} \mathrm{~N}$
(b) $13 \times 10^{-6} \mathrm{~N}$
(c) $107 \times 10^{-7} \mathrm{~N}$
(d) $103 \times 10^{-7} \mathrm{~N}$

Key Concepts

Effects of Absorption and Reflection

When radiation hits a surface, the way in which the surface interacts with the light (either absorbing or reflecting it) determines the momentum transfer. An absorbed photon transfers its momentum fully, while a reflected photon effectively reverses its momentum, resulting in roughly twice the momentum change. This distinction is critical when calculating the net force on surfaces with partial reflectivity and absorptivity.

Force Calculation from Radiation

The overall force delivered by radiation on a surface is calculated by considering the power of the incident radiation and modifying it according to the efficiency of momentum transfer due to absorption and reflection. The total force is found by adding the contributions from both processes, using the relationships F_absorbed = P_absorbed/c and F_reflected = 2P_reflected/c, then summing these results.

Radiation Pressure

Radiation pressure is the pressure exerted by electromagnetic radiation upon any surface due to the momentum carried by the photons. It is calculated using the relationship between the power of the incident radiation and the speed of light, typically as force per unit area, and plays a crucial role when dealing with light-matter interactions.

Momentum Transfer by Photons

This concept involves understanding that photons, despite being massless, carry momentum given by p = E/c, where E is the photon energy and c is the speed of light. The transfer of this momentum to a surface when photons are absorbed or reflected is what results in a mechanical force acting on that surface.

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