Radiation force on a solid hemisphere

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SUMMARY

The discussion focuses on calculating the force exerted by a parallel beam of light on a perfectly reflecting solid hemisphere with radius R and intensity I. The relevant equation for radiation pressure is given as radiation pressure = I(1 + ro)(cos^2(x))/c, where ro is the reflection coefficient, x is the angle of incidence, and c is the speed of light. With ro set to 1, the force on the hemisphere is determined to be less than that on a disc of the same radius, specifically less than 2πr²I/c. The solution involves integration to account for the varying impulse components across the hemisphere.

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  • Understanding of radiation pressure and its formula
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  • Familiarity with the concept of reflection coefficients
  • Basic principles of optics and light behavior
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Krushnaraj Pandya
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Homework Statement


A perfectly reflecting solid hemisphere of radius R is placed in the path of a parallel beam of light of large aperture, if the beam carries an intensity I, what is the force exerted by the beam on the hemisphere?

Homework Equations


radiation pressure=I(1+ro)(cos^2(x))/c
I is intensity, po is reflection coefficient, x is angle of incidence and c is speed of light.

The Attempt at a Solution


ro=1 here, Intuitively the force will be less than on a disc of the same radius, so it is less than 2*pi*r*r*I/c, I also know integration will be involved but I can't figure out how to go about it. I'd appreciate some help, thank you
 
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Krushnaraj Pandya said:
integration will be involved
For any particular photon, what component of the impulse it applies is relevant?
Consider an element of the hemisphere over which that component is approximately constant.
 

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