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The incident intensity on a horizontal surface at sea level from the sun is about 1 $KWm^{-2}$. Assuming that 50 percent of this intensity is reflecting and 50 per cent is absorbed, determine the radiation pressure on this horizontal surface (in pascals).
A) $8.2 \times 10^{-2}$
B) $5 \times 10^{-6}$
C) $3 \times 10^{-5}$
D) $6 \times 10^{-5}$

Last updated date: 11th Jun 2024
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Hint: Radiation pressure exerted because of momentum and electromagnetic field.
Radiation pressure is given as:
$P = \dfrac{{\left( {1 + e} \right)I}}{c}$ (P is the radiation pressure, e is the percentage of light intensity reflected and I is the incident intensity, c is the speed of light).
Using the above relation we will find the radiation pressure.

Complete step by step solution:
Let’s first discuss radiation pressure and its effect and then we do the calculation part.
Radiation pressure, the pressure on a surface resulting from electromagnetic radiation which has an effect on it that is a result from the momentum carried out by radiation. Radiation pressure is doubled if the radiation is reflected rather than absorbed.

A very simple definition of radiation pressure is that electromagnetic pressure exerts a minute pressure on everything it witnesses in its path is called radiation pressure. When light is reflected on a mirror is subject to some radiation pressure.
Let us now do the calculation part of the problem.
$ \Rightarrow P = \dfrac{{\left( {1 + e} \right)I}}{c}$...............(1)
We will substitute the numerical values of each term in equation 1, we will take the value of c velocity of light as 3$ \times 10^8$.
   \Rightarrow P = \dfrac{{\left( {1 + 0.5} \right)1000}}{{3 \times {{10}^8}}} \\
   \Rightarrow P = \dfrac{{1500}}{{3 \times {{10}^8}}} \\
 $(e is given 50% which is 0.5)
$ \Rightarrow P = 5 \times {10^{ - 6}}$ Pascal

Note: We have various applications of radiation pressure which includes laser; solar sails have been developed for the propulsion of the spacecraft, beam powered propulsion of spacecraft may be realised with high power lasers. Light forces have been achieved which strongly affects the dynamics of small particles.