I added the "all rays" construction because I simply could not understand what was happening via a standard [i]ray diagram[/i]. Of course the [i]ray diagram[/i] gives you all the [b]numbers[/b] for calculating, but I could not understand what was happening when only the 2 "determining" rays were being shown to me. I did not understand that light rays were coming out in all directions from the object point like the sun; that the ones that hit the lens were refracted (the other ones just continue on their merry way) and that this refraction was focused onto an image point which was determined by the 2 rays (i.e. the focus ray and the center ray).
I also found it hard to transfer even this construction into an understanding of an object point and a lens in 3D. I am waiting for GeoGebra 3D to allow one to draw 3D ellipses. Then I will work on a 3D version so that a student can see that: (a) one takes (0,0)=center of the lens and constructs a plane normal to the lens and passing through (0,0) and P=object point and then (b) marks the line passing through (0,0) and F as the x-axis (and of course the y-axis normal to this x-axis).
Credits: This worksheet is a combination of my understanding from Sal Khan's video on lenses and Mark Crookes' construction video at http://carefuluncertainty.blogspot.com/2011/09/geogebra-physics-tips.html. Of course though, any mistakes or misunderstandings are purely mine. Please advise if you find anything wrong :)
