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Set 54 Problem number 5


Problem

A sunbeam with intensity 1.8 watts / m^2 shines through a square window .6 meters on a side.  The beam makes an angle of 64 degrees with normal to the plane of the window.  What is the power flux through this window?

Solution

The area of the window is ( .6 m) ^ 2 = .36 m ^ 2, so the flux of a perpendicular 1.8 watt/m ^ 2 beam would be

The 64 degree angle means that less light passes through the window.  The proportion of the change is cos( 64 deg) = .4392, so the flux is

Generalized Solution

The power flux of an energy intensity `intensity (typically measured in Watts/square meter) intercepted at a perpendicular by an area A is simply

If the beam makes angle `theta with the perpendicular, then flux is reduced according to the cosine of the angle:

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