Linearity in optics

This may be a dumb question, but...

Say you have a 6" f10 lens. At the objective, the light path is 6" in diamter; 60" away, at the focus, it's an infinitely small point. My question: is the relationship between diameter of the light path and distance from the objective linear? For example, at 30" from the objective, will the light path be 3" in diameter? At 20" from the objective, will it be 4" in diameter?

I'm working on a folded refractor project, and I need to figure the size of the flat and the distance from the objective. Haven't decided on the size and f-ratio of the objective yet, so I was hoping for the theory, rather than the specific practical application.


Jeff Verona

Yup, it's linear. Diameter of the light cone will vary in direct proportion to the distance you've traveled down the focal length.

It's only infinitely small at the focal point if the objective is optically perfect, of course ;-)

Hi Jeff --

I've always taped a few sheets of paper together and drawn a line perpendicular to the lens thru its midpoint and then drawn converging lines to meet at its focal length. Doing this gives me a better 'gut' feeling about needed baffle sizes/locations.
Good luck with your project.

Bob Polcyn