Basic theories in telescopes (Telescopes-part 3)

What are the basic theories on telescopes? How do we do the calculations related to
telescopes? If you need to know those things, you must read this article.
In a telescope, also a camera too, there is a power of light gathering. We characterize it with
ratio, called focal ratio. The equation is as follows,

We denoted the focal ratio as f/n, n is the focal ratio. For example, if we have a telescope with a
focal ratio of 8, we denote it as f/8.
if the focal ratio is smaller, we describe it as a “fast” telescope. This means that one can take
photographs using short exposures since the image is bright. The telescopes which have a
smaller focal ratio, their focal length nearly equal to the diameter of the objective, aperture.
In the telescopes that have a higher focal ratio, their length of the telescope tube is a lot longer
than the aperture and we call them “slow” telescopes.
When we consider the magnification of a telescope, the higher focal ratio telescopes have
larger magnification than smaller ones to a given aperture.
How do we find the magnification of the telescope? The equation is as follows.

From the above equation, we see how magnification is proportional to the focal length of the
aperture to a given aperture and eyepiece.

Usually, in telescopes that have smaller focal ratios, their apertures are more curved than the higher ones. So, when we are talking about optical distortion, the telescope that has smaller focal ratios have more optical distortion than higher focal ratio telescopes. Because they suffer from “Chromatic aberration” and for those telescopes which have smaller focal length than the aperture, they are suffering from significant distortions at the edges of the field of view.

Now you are thinking about some words that unfamiliar with you above mentioned. What is chromatic aberration?  What is the field of view (FOV)? I will describe chromatic aberration on the heading of telescope errors.

What is the Field of View (FOV)?

The field of view (FOV) is the circle of sky visible through the eyepiece. For example, if you change your eyepiece to get larger magnification, the field of view is getting smaller. You can understand now, magnification of the telescope gets larger, the field of view is getting smaller.

They are inversely proportional. Before we calculate the field of view of your telescope, we need to know some important words.

Apparent field of view:

This is describing how much of the sky we can see when looking through the tube of the eyepiece when it is not attached to the telescope. This measurement is already measured by the manufacturers because this is a constant value. 

Actual/true field of view:

             True FOV how much you can see the sky with the eyepiece in a static place.

How can we calculate the true field of view? 

This is how we calculate the field of view. This is measured by radians. 

The resolving power

The resolving power is more important characteristics that depend on the aperture of the telescope. We have to use this like calculations including binary star systems. It means, if we want to see the stars separately in a binary system, you have to configure the minimum angle resolution for that. If know that, we can choose a telescope for it. How to find the angle resolution of the telescope,

The resolving power is more important characteristics that depend on the aperture of the telescope. We have to use this like calculations including binary star systems. It means, if we want to see the stars separately in a binary system, you have to configure the minimum angle resolution for that. If know that, we can choose a telescope for it. How to find the angle resolution of the telescope,

𝛌= wavelength of the star in spectral class D= diameter of the objective

You can use this not only to an optical telescope but also to any other wavelength telescope. We can see two objects separately when,  𝜃 ≥ ^𝛌⁄𝐷 . 

I think you got a big idea about those concepts on telescopes. If there is any question in this article you can ask it in the comments section. In the next article, I will bring you what are the errors that occur in telescopes and about the big bang.

Author: Induwara Bandara

References:

1. Fundamentals in astronomy, by H. Karttunen, P. Kröger, H. Oja, M. Poutanen, K. J. Donner
2. https://lovethenightsky.com/what–is–a–field–of–view–in–astronomy–and–why–is–it–useful/
3. https://skyandtelescope.org/observing/skyandtelescope–coms–scopecalculator/#:~:text=Magnification%20(power)%3A%20The%20amount,twice%20its%20aperture %20in%20millimeters).