The focal point is where rays will be focussed to/from a parallel beam of light - like the rays from an object at infinite distance. The theory is normally quoted in these terms, as it avoids having to consider two distances at once (the distance to the object and the distance to the image or observer). Thus:
/ Parallel rays from a distant object / <---------------------------------------- | | + Are all focussed to here | (the focal point, by definition) \ <---------------------------------------- \ ... but in real life, the object will be nearer than infinity ... / / Non-parallel rays from nearby object (O) | | + I O | \ Are focussed to an inverted real image somewhere else (I) \ ... and as the object moves closer to the mirror, the image of it moves further away, and crosses over the object position (at the point where, looking into the mirror, you find the image of your eye disappearing into a singularity) and continues to move further away until ... / / ----------------------------------------> | Rays from an object at the focal point (O) | O | \ ----------------------------------------> \ Are "focussed" to infinity ... you get back to an easy-theory situation. The geometry of the intermediate positions is probably something like: (1 / distance_to_object) + (1 / distance_to_image) = (1 / focal_length) ... at least qualitatively. I don't know whether that is correct quantitatively. I hope this was the "clue to the obvious" that you needed. - Julian "Curtis L. Olson" wrote: > > Ok, this is *way* off topic, but I'm hoping the people here are a bit > smarter than my stupid coworkers (I guess stupid _self_ is implied.) > > :-) > > The following web site explains the basic behavior of a concave mirror > and pretty much agrees with everything I remember from physics: > > http://www.physicsclassroom.com/Class/refln/U13L3a.html > > If the object distance is beyond the focal point, the reflected image > will be inverted. If the object is at the focal point, the reflected > image will hit a singularity. If the object distance is less than the > focal length, the object will be magnified and right-side up. > > Now, I have a concave mirror with a 40" radius of curvature. This > means it has a 20" focal length. My problem is that I'm not observing > behavior that matches the theory. > > My initial speculation is that the position of my eye is an important > factor that isn't addressed by the simple theory, but from the simple > theory, I don't see how that could be possible. > > Here are some things I'm observing: if my eye is closer to the mirror > than the focal distance, I see myself and the entire room right side > up. Even though objects in the distance (i.e. the other side of the > room) are further than the focal point, they are still right-side up. > > If I move my eye point away from the mirror and watch myself, I seem > to hit the singularity at 40" which is the center of curvature, not > the focal point. Yes, I've verified that the radius is indeed 40" and > is most definitely not 80". > > If my eye point is further than 40" I can move an object (such as a > pen in and out and it hit's the singularity at 40" and inverts beyond > that.) > > If I move my eye away from the mirror and watch an object on the > otherside of the room, it hits the singularity and inverts at 20". > This sort of agrees with the above theory except it's a distant object > that never moves, only my viewpoint is moving. ?!? > > I've been trying to reconcile this all in my head and have put myself > into a state of complete befuddlement ... > > Can anyone tell me what stupid thing I am missing? > > Curt. > -- > Curtis Olson IVLab / HumanFIRST Program FlightGear Project > Twin Cities [EMAIL PROTECTED] [EMAIL PROTECTED] > Minnesota http://www.menet.umn.edu/~curt http://www.flightgear.org > > _______________________________________________ > Flightgear-devel mailing list > [EMAIL PROTECTED] > http://mail.flightgear.org/mailman/listinfo/flightgear-devel _______________________________________________ Flightgear-devel mailing list [EMAIL PROTECTED] http://mail.flightgear.org/mailman/listinfo/flightgear-devel
