Determine Radiation pressure given the fraction of total absorption

In summary, the problem involves radiation of intensity I normally incident on an object that absorbs a fraction frac and reflects the rest back along the original path. The radiation pressure on the object can be calculated using the equations Pra = (frac)*I / c and Prr = 2*(1-frac)*I/c, which can be combined to find the total pressure of (2-frac)*I/c.
  • #1
MrMoose
23
0

Homework Statement



Radiation of intensity I is normally incident on an object that absorbs a fraction frac of it and reflects the rest back along the original path. What is the radiation pressure on the object?

Homework Equations



Radiation pressure Pr (force/unit area)

Pra = I/c (total absorption)

Prr = 2I/c (total reflection back along path)

The Attempt at a Solution



The object absorbs a fraction frac of the intensity, which I translate mathematically as:

Pra = (frac)*I / c

This would mean that the total intensity reflected is:

Prr = 2*(1 - frac)*I/c

Unfortunately the answer is: Pra = (2 - frac)*I / c

I don't know how they came to this conclusion. Thanks in advance, MrMoose
 
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  • #2
So how do you go from Pra and Prr to total pressure?
 
  • #3
Holy smokes. Thanks.

Pra + Prr = (frac)*I/c + 2*(1-frac)*I/c = I*frac/c + 2*I/c - 2*frac*I/c

= (2 - frac)*I / c
 

FAQ: Determine Radiation pressure given the fraction of total absorption

1. What is radiation pressure?

Radiation pressure is the force exerted by electromagnetic radiation on a surface or object. It is caused by the transfer of momentum from the photons of light to the surface they strike.

2. How is radiation pressure calculated?

Radiation pressure can be calculated using the equation P = F/A, where P is the pressure, F is the force exerted by the radiation, and A is the area of the surface receiving the radiation.

3. How does the fraction of total absorption affect radiation pressure?

The fraction of total absorption plays a crucial role in determining radiation pressure. It is a measure of how much of the incident radiation is absorbed by the surface. The higher the fraction of total absorption, the greater the radiation pressure will be.

4. What is the relationship between radiation pressure and the color of light?

The color of light does not directly affect radiation pressure. However, different colors of light have different wavelengths and energies, which can impact the force exerted by the radiation and thus affect the overall radiation pressure.

5. How is radiation pressure used in scientific research?

Radiation pressure is a fundamental concept in various fields of science, including astrophysics, optics, and material science. It has practical applications in areas such as laser propulsion, particle acceleration, and solar sails. Scientists also use radiation pressure to study the properties of light and its interactions with matter.

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