How to Calculate Telescope Field of View
Calculating the field of view (FOV) of a telescope is an essential step for astronomers and hobbyists alike, as it helps determine what celestial objects can be observed through the telescope. The field of view is the area of the sky that the telescope can cover at a given magnification. In this article, we will discuss the formula to calculate the field of view and the factors that affect it.
The formula to calculate the field of view is:
FOV = (2 tan(θ/2)) focal length
Where θ is the angular diameter of the telescope’s objective lens or mirror, and the focal length is the distance from the objective lens or mirror to the focal plane.
To find the angular diameter, you need to know the diameter of the telescope’s objective lens or mirror. The angular diameter can be calculated using the following formula:
θ = 2 arctan(diameter / 2 focal length)
Where diameter is the diameter of the objective lens or mirror, and focal length is the distance from the objective lens or mirror to the focal plane.
Let’s consider an example. Suppose you have a telescope with a 100mm objective lens and a focal length of 1000mm. First, calculate the diameter:
diameter = 100mm
Next, calculate the angular diameter:
θ = 2 arctan(100mm / (2 1000mm)) ≈ 0.0523599 radians
Now, use the formula to calculate the field of view:
FOV = (2 tan(0.0523599/2)) 1000mm ≈ 2.8°
This means that the field of view of the telescope is approximately 2.8 degrees. To convert this to arcminutes, multiply by 60:
FOV ≈ 2.8° 60 ≈ 168 arcminutes
Keep in mind that this calculation assumes a perfect telescope with no optical aberrations. In reality, the actual field of view may be slightly smaller due to factors such as atmospheric seeing, telescope collimation, and optical aberrations.
In summary, calculating the field of view of a telescope involves determining the angular diameter of the objective lens or mirror and multiplying it by the focal length. This formula provides a rough estimate of the field of view, which can be adjusted for real-world conditions. By understanding the field of view, astronomers and hobbyists can better plan their observations and choose the appropriate telescope for their needs.
