Vignetting


Pupils will carry out percentage calculations to find out how much light is lost as a result of a telescope's support structure for the secondary mirror.

Resources required

Perspective diagrams of the Liverpool Telescope, which you can find HERE.

Compasses and calculators.

It is recommended that pupils experience operating a model of the Liverpool Telescope model (LT3D) to investigate the construction of the instrument and identify its main components. For more information about this software click HERE.

Content

  1. Explain to the students the most basic meaning of vignetting (i.e. reduction of a telescope's light-gathering capacity by virtue of its own physical structure).
  2. Show them an image of the Liverpool Telescope and ask them how they might model the effect.
  3. Invite them to draw a sketch of the situation. They should come up with something like Fig 1.

    4. Liverpool Telescope showing secondary mirror and supports. fig 1

  4. Ask them now how they would model the obstructions. Discuss what variables will come into play.
  5. Ask them to find the area of each of the rectangles, the area of the large circle and the area of the small circle.
  6. They can calculate the obstructed area and express this as a percentage of the total area.
  7. Clearly this is just one case. Can they now generalise it?
  8. Help the students to develop the following results:
    Arect = w(R - r)
    		 AC = πR2
    		Ac = πr2
    		V = (Ac + 4Arect)/AC
  9. Express V as a percentage of AC.
  10. Use a graph to plot V against w for a variety of values of R and r.
  11. Discuss the vignetting effect of the secondary focus relative to that of the stanchions supporting it.
Keywords

Vignetting, circles, percentages, area

Teachers' Notes

  1. The radius of the primary mirror is R. The radius of the secondary mirror assembly is r.
  2. Each mirror support is rectangular with width w, length R - r and area Arect.
  3. The area of the "big circle" (primary mirror) is AC, that of the "little circle" (secondary mirror) is Ac.
  4. Pupils need to know how to find the area of a circle.
  5. Pupils need to know how to express one quantity as a percentage of another.
  6. The diameter of the primary mirror in the Liverpool Telescope is 2 metres.
  7. The diameter of the secondary mirror assembly is 0.85 metres.
  8. The width of the mirror supports is 7 millimetres.

The National Schools' Observatory wishes to thank
Carl Sanderson for writing this page of the Staffroom.


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