A parallel beam of light is incident normally on a plane...

A parallel beam of light is incident normally on a plane surface absorbing $40 \%$ of the light and reflecting the rest. If the incident beam carries $60 \mathrm{~W}$ of power, the force exerted by it on the surface is (a) $3.2 \times 10^{-8} \mathrm{~N}$ (b) $3.2 \times 10^{-7} \mathrm{~N}$ (c) $5.12 \times 10^{-7} \mathrm{~N}$ (d) $5.12 \times 10^{-8} \mathrm{~N}$

A parallel beam of light is incident normally on a plane surface absorbing $40 \%$ of the light and reflecting the rest. If the incident beam carries $60 \mathrm{~W}$ of power, the force exerted by it on the surface is
(a) $3.2 \times 10^{-8} \mathrm{~N}$
(b) $3.2 \times 10^{-7} \mathrm{~N}$
(c) $5.12 \times 10^{-7} \mathrm{~N}$
(d) $5.12 \times 10^{-8} \mathrm{~N}$

Key Concepts

Radiation Pressure

Radiation pressure is the pressure exerted by electromagnetic radiation on a surface due to the transfer of momentum when light is absorbed or reflected. It is a fundamental concept in understanding how light can exert force on objects, and it is directly related to the energy and momentum of the light beam.

Momentum Transfer in Light

Light carries momentum even though it is massless, and this momentum is related to its energy by the relation p = E/c. When light interacts with a surface, the change in momentum (depending on whether the light is absorbed or reflected) results in a force on that surface.

Conservation of Momentum

The conservation of momentum principle is crucial in analyzing the interaction of light with surfaces. When light is absorbed, its momentum is transferred to the surface, and when it is reflected, the momentum change is typically larger, effectively doubling the momentum imparted compared to absorption. This concept allows for the calculation of force based on the change in momentum over time.

Power-Energy Relationship in Radiation Forces

The power of a light beam is the rate at which it delivers energy, and since energy and momentum are linked for electromagnetic radiation, power can be used to determine the force exerted by the light. This involves calculating the momentum transferred per unit time using the light’s energy divided by the speed of light.

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