[email protected] wrote: > [email protected] wrote: > >[email protected] wrote: > >> Trevor Sheppard > >> <[email protected]> wrote: > > > >[regarding focusing of light by bullseye rooflights] > > > >> I've heard tell that this problem can occur only if the bullseye is > >> incorrectly installed, which is a common mistake. > >> AIUI, the bullseye should be installed with the curved (convex) side > >> *down*. This lights the interior better, by dispersing the light. If > >> the bullseye is installed the other way up, it concentrates the light > >> (and heat) on a point in the interior. > > > >I've heard that too, but I'm unconvinced. My memory from studying physics > >(quite as long time ago, admittedly) is that the paths taken by light rays > >passing through a lens are 'reversible'; in other words if a lens converges > >light passing through it in one direction, then it will also converge light > >passing through it in the opposite direction. > >Or have I remembered it wrongly? > I think you may have. > Draw a vertical cross-section of the bullseye. Orient it so the > convex side is up. Now draw a sun's ray hitting it vertically from > above. My memory of physics is that the ray will be redirected from > the vertical when it hits the bullseye, in the direction that brings > its angle with the surface of the bullseye at the point of > intersection nearer to the perpendicular to that surface.
Yes, it is refracted towards the perpendicular if it enters a more optically dense (higher refractive index) material, and away from the perpendicular if it does the opposite. They will > be further deflected when they leave the bullseye Correct. It is being bent away from the perpendicular this time, but we're now talking about the perpendicular to the flat side, and the upshot is that it is bent further in the same direction that it has already been bent. (this is where it gets useful to draw a diagram) > Assuming that, then draw some other angles, which will show that the > redirected rows get concentrated (i.e. focused). No problem with that. > Now orient the bullseye with the flat side up, and draw some more > rays. These will pass straight through the flat surface, No problem with that, either. but will be > bent away from the centre of the bullseye when they leave it. That's where it goes wrong. They will be refracted away from the perpendicular as they are entering a less optically dense medium. That means they are bent towards the centre of the bullseye. > I think this means that they can burn in the first case, but can't in > the second. If there's any truth in that, then it's nothing to do with the basic optics of how light passes through a plano-convex lens. A converging lens is a converging lens in both directions. Martin L
