Oktay Mercimek, EMAT 6690
Step 4 : Newton Telescope
Newtonian telescopes have a parabolic mirror and a flat mirror.
Parabolic Mirror collects light rays at its Focus, and Flat Mirror helps us to direct these light rays from focus of the parabola to outside of the Telescope.
How to build this telescope with GSP ?
1. We need two parallel rays to be sides of telescope, a directrix line that is perpendicular to these rays and a focus point for the parabola
We need to create light rays that is perpendicular to the directrix. At this point, we need prepare ourselves to the flat mirror because this mirror will block some of the light rays to reach parabolic mirror.
So I placed a flat mirror between focus and the directrix of the the parabola. That's why only light rays that is coming between "Point E and Point F" and between "Point G and Point H" can reach to the directrix.
Drag Point C to see which rays can reach to directrix. In fact I created two separate rays that both of them are perpendicular to directrix. (Therefore we may need to construct some step separately for these two rays)
(Following the parabola construction from the first page).
Now we can continue to construct our parabola. We need a segment that connects Points C and Focus of the parabola. After that we need to construct the perpendicular bisector of the segment.
As we learned in the first page, Triangle(PCJ) is a isosceles triangle and PJ=JC. Therefore Point J is on the parabola.
The locus has a missing part in the center due to two separate lines that I mentioned before.
Since we constructed the parabola, we can construct the reflection property of the parabola.
This parabola will send light rays to Focus point from Point J.
Assuming there is no flat mirror would result like:
we know there is a flat mirror and that mirror will reflect these rays, and we can use circle trick to demonstrate this flat mirror.
Did you see where we should place the flat mirror?
Drag Focus point to understand the role of this point.
Click here to go to Step 5: Ellipse and Hyperbola