# Why are telescope mirrors nearly flat?

My understanding of telescope mirrors is that they are (generally speaking) a slice out of an imaginary sphere. The center of this sphere is the focal point of the telescope, where the detector is placed. The bigger the sphere, the further away the focal point will be.

With this in mind, why are telescope mirrors nearly flat? Would it not make sense to instead use the same diameter mirror, but with a smaller imaginary sphere so the detector doesn't have to be so far away?

I have made a crude image to demonstrate my point. The blue arc and point represent a more traditional "nearly flat" mirror, whereas the red arc and point represent a mirror that has the same diameter but with a smaller sphere and therefore closer detector.

The main reason is that the red mirror produces a smaller image in its image plane, which requires a smaller pixel spacing in the detector (or a stronger eyepiece) to get the same resolution.

In a Newtonian telescope the focal length cannot be too small:

(Image Krishnavedala)

Also, a more ideal shape is a paraboloid (not a sphere). Spherical mirrors are relatively easy to manufacture, and "nearly flat" ones are very close to paraboloids.

• Can you add a bit of an explanation as to what the picture shows? I figure it's showing some reason for why the focal length can't be too small, but I don't comprehend from the diagram alone how it demonstrates this. – Drake P Dec 2 '20 at 19:19
• @DrakeP If you try to draw that with a shorter focal length, you will find that the diagonal mirror must be larger, blocking the incoming light. This is not so much an issue with the professional class scopes discussed by Rob Jeffries, which have a CCD detector instead of the mirror. – Keith McClary Dec 2 '20 at 22:25

Fast mirrors (low f ratio) such as the red mirror in your illustration, are more subject to aberrations, principally coma. Coma is the effect that circular or point like objects that are off the optical axis do not form uniform circular images, blurred in a coneshape image. It is possible to correct for this using additional optical components, but this adds complexity and expense.

Most modern telescopes do have very small f-ratios. i.e. The focal length is not a large multiple of the mirror diameter.

The main advantage of this is that you don't have to build a massive dome to house your telescope in and you also get a larger field of view.

For example, the VLT telescopes at Paranal have a diameter of 8.2-m and a focal length of just 14.4 m. The mirrors are about 20cm thick and weigh nearly 20 tonnes.

The reason that this was not done in the past is I think that a highly curved miror has to be thicker and so it becomes difficult to make such a thing without it deforming under its own weight as you move the telescope about. Some of these problems have been partially solved using various material technologies as well as active mirror supports.

However, these problems still remain and the next generation of large telescopes will use segmented mirrors, which gets around the size/weight problem whilst still allowing high degree of curvature to the overall mirror and hence minimises the size of the telescope and the building it is housed in. Of ourse you then have the technological problem of keeping all the different parts aligned to a fraction of the wavelength of light.

For smaller telescopes, there are now an increasing number of low f-ratio designs which offer portability and a wider field of view. The disadvantages are that you need a bigger CCD and/or smaller pixels to tile the field of view and it it is more difficult to make highly curved mirrors that are free of problems like coma and astigmatism away from the centre of the field.