How to Calculate Telescope Magnification

The magnification of a telescope is the ratio by which the telescope is used to enlarge the object you are looking at. Generally speaking, the maximum magnification a telescope is capable of is the aperture in inches multiplied by 50 (or the aperture in millimeters multiplied by 2).

This changes depending on what eyepiece is attached to the telescope. The eyepiece is used to magnify the image and can be changed to suit.

The formula to work out magnification of a telescope is

Telescope focal length / Ocular focal length = Magnification

Aperture

This is the name for the gap in the telescope that light can travel through. The aperture size is the diameter of this gap (assuming it is circular). 

For refracting telescopes, this is the diameter of the objective lens. For reflecting telescopes, this is the diameter of the primary mirror. 

The larger the aperture on a telescope, the more light is absorbed through it. This means that the limiting magnitude (the faintest object you can see) of the telescope is lessened.

As the aperture of the telescope increases, the field of view becomes narrower. The resolving power increases with the aperture.

This is sometimes worked out using the formula

f / # =f / D

f denotes the telescope’s focal length and D denotes the aperture diameter. They are measured using the same units.

Field of View

This refers to the area of the night sky that you can see through your telescope. In other words, it is the span of the image you can see in the eyepiece. At a high magnification, the field of view is smaller. This is because you are essentially zooming in on an area of the sky. 

The image width is measured in angles to give you the field of view. An eyepiece typically has a 50 to 60 degree field of view. Wide-field eyepieces tend to top out at around 80 degrees, but can go up to 100 degrees.

The field of view decreases in line with the magnification of the telescope’s eyepiece. If you increase the magnification by a factor of 10, your field of view will be one tenth of the original. 

To work out the field of view, you will need to work out the field of view of the eyepiece, and then divide that by the magnification of your scope.

Field of view (scope) = Field of view (eyepiece) / magnification

Image Resolution

This is the level of detail that you will be able to discern at varying levels of magnification, i.e. how far apart 2 stars must be so you can tell they are separate. This is measured in a unit known as arcseconds. 

The human eye is capable of distinguishing between objects 120 arcseconds apart. This means that the telescope must magnify stars to this distance apart from one another. To find the resolution of the image, use the formula below. 

Resolution = 120 / Magnification

Focal Length

This is the distance between the mirror (or primary lens) of a telescope and the point where the rays of light converge and focus. This is measured in millimeters. In layman’s terms, this is the point at which the image appears in focus once you have adjusted the distance between the lens and your eye. 

All telescopes have a fixed focal length, like a camera lens. The lower the millimeters of the focal length, the wider your field of view. A 300mm focal length will have a smaller viewfield than a 10mm, although the magnification will increase with the focal length, making the object you are looking at appear larger. 

This differs between telescopes as it relies on the type of telescope and the length of the interior tubing. It often tends to fall just inside the tube or focuser. Eyepieces are attached to the end of the tube to help our eyes focus on the focal point. 

Eyepieces 

The focal length of an eyepiece should be stated clearly on the outside of the tubing. It will be one of 4 lengths - 6mm, 20mm, 30mm, and 40mm. 

You should also focus on the exit diameter of the eyepiece. Smaller diameters mean that it can be difficult to see highly magnified objects. For beginners, we recommend purchasing a wide-angled eyepiece to make viewing easier. 

Working Out the Magnification

Let’s assume, for the sake of this explanation, that the focal length of your telescope is 1,000mm. Let’s multiply this by all of the different focal lengths of the eyepiece.

You should always use measurements in millimeters when working out the magnification of a telescope. Sometimes the measurements you have to hand will be in inches or centimeters, but we recommend converting them to millimeters first, as it will make your life much easier.

To convert inches to millimeters, multiply the value by 25. For centimeters to millimeters, multiply the number by 10.

1000 / 6 = 167x magnification

1000 / 20 = 50x magnification

1000 / 30 = 33.3x magnification

1000 / 40 = 25x magnification

This shows that the smaller the focal length of the eyepiece, the larger the magnification will be. A 6mm ocular focal length combined with a 1,000mmm telescopic focal length will magnify whatever you are looking at by 167 times. 

What is a Barlow lens?

This is a special, concave lens to place inside the telescope before the eyepiece is inserted. There are many different sizes, which can adapt the focal length of the telescope. The most common is the 2x Barlow lens which doubles the focal length. 

Barlow lenses were created by an English mathematician known as Peter Barlow in the late 18th century. They will not only increase the magnification of your telescope, but it will also make it much more versatile.

You can use the telescope with or without these lenses and so by owning them, you essentially double your range of magnifications. 

Barlow lenses will not only magnify what is in the viewfinder of your telescope, but will also amplify light pollution, dust, pollen, and anything else. 

Gordon Watts
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