Re: radiometer paradox

[jriley@lib.drury.edu (Jim Riley)]

Joseph Gress Wrote:

> I am puzzled by how a radiometer works.  It makes sense to me that 
> when you shine light on the black fin that radiation pressure would 
> cause the radiometer to spin.  However, why doesn't it spin even 
> faster when you shine light on the white fin?  In fact, it doesn't 
> spin at all!   If  I think of 
> reflection as a photon of light bouncing off of the white 
> fin, then the change in momentum of the photon would be twice as 
> great as if the photon were absorbed.  
>
> I looked up radiation pressure in several text books.  The closest 
> example indicated that radiation pressure = the light irradiance 
> (watts per m^2) /  speed of light; i.e.  P=I/c if the light is 
> completely absorbed whereas P=2I/c if the light is reflected.  This 
> matches my simple picture of what I thought was happening when light 
> hits the radiometer fins.
>
> So, why doesn't light shining on the white fin (which is reflected) cause
it to spin 
> faster than light shining on the black fin (which is absorbed).
>
> Joseph Gress
> **************************************
>
> Sincerely,
> Joseph Gress
> Department of Physics and Astronomy
> Moorhead State University
> Moorhead, MN 56563
> e-mail: gress@mhdha.moorhead.msus.edu


This is a nice example of something not working the way it is "supposed to
work".  A simple analysis assuming that light is a particle would indicate
that the pressure on the white side should be greater than that of the dark
side and therefore the radiometer ought to spin with the white side
trailing.  It doesn't.  If it spins at all it spins with the dark side
trailing.  There is a very nice PSSC film demonstrating this phenomena and
its explanation but I don't remember the name of the film.  

The explanation is that the spinning effect is due to residual air in the
radiometer and not the impulse given by the impact of light.  The dark side
heats up more than the light side.  Air molecules coming into contact with
either side are struck harder by the more quickly moving warm molecules in
the surface of the dark side than those of the colder white side.  The
greater resulting reaction force on the dark surface causes the radiometer
to spin with that side trailing.

To show that this is in fact the cause a radiometer in the film is pumped
out to much lower pressure than normal.  The radiometer does not spin at all
now.  There are not enough air molecules present to produce much of an
effect and there is too much friction in the bearings to allow the impact of
the light to turn the radiometer.

The film takes the experiment one step further by suspending a small piece
of metal from a very fine fiber in a high vacuum.  A bright light is shined
repeatedly on the metal at intervals matching the "pendulum" frequency of
the metal and fiber and the metal is set in motion.  

I would assume that this film is still available probably on one of the
laser disk collections of "Physics Classics".  It is a good film in that it
answers a significant question in a way that the individual instructor would
have a difficult time doing on her/his own.
Jim Riley, Department of Physics
Drury College
900 N Benton Ave.
Springfield, MO 65802
e-mail: jriley@lib.drury.edu
Phone:  (407) 873 7233