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


This page uses JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright © 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial use.

Sorry, this page requires a Java-compatible web browser. Newton1.gsp

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.

Sorry, this page requires a Java-compatible web browser. Newton2.gsp

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.

Sorry, this page requires a Java-compatible web browser. Newton3.gsp

 

As we learned in the first page, Triangle(PCJ) is a isosceles triangle and PJ=JC. Therefore Point J is on the parabola.

Sorry, this page requires a Java-compatible web browser. Newton4.gsp

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:

Sorry, this page requires a Java-compatible web browser. Newton5.gsp

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.

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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

Click Here to proceed Step 3: Parabola Reflection Page

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