I follow Jack's logic, except that I get that the energy density
is proportional to D^4, rather than having D cancel out.
A larger diameter focuses more energy into a smaller area.
Daniel Crowe
Oklahoma School of Science and Mathematics
Ardmore Regional Center
dcrowe@sotc.org
________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu on behalf of Jack Uretsky
Sent: Sun 4/16/2006 3:18 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] fire starter from the sun
Heere's my analysis: We're not focussing the sun's image, we are
placing the focal point of the rays from the sun on the fuel. The rays
focus to an angle of about lambda/D radians, at a distance f from the
lens, where lambda is the average wavelength, D is the diameter of the
lens, and f the focal distance of the lens. The spot radius is therefore:
(lambda/D)f
and the area is the square of this quantity (time pi). The energy
concentrated is proportional to D^2, so the lens diameter cancels out, and
the energy density in the spot is inversely proportional to f^2. Short
focal-length lenses (thick lenses) work better - which accords with my
memories of childhood.