# Radiation force on a solid hemisphere

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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

## Answers and Replies

haruspex
Science Advisor
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Gold Member
2020 Award
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.