In astronomy, the magnitude refers to a **logarithmic** measure of the brightness of a celestial body. The **larger** the magnitude number, the **fainter** the object. The magnitude has no unit.

The **limiting magnitude of a telescope** is the brightness of the dimmest object that can still be seen with a particular telescope. A substantial value of limiting magnitude of a telescope means that even a very faint object can be seen.

The value of the limiting magnitude depends on:

- the telescope’s
**objective diameter**and - observer’s eye entrance
**pupil**.

__It can be calculated using the formulas listed below: __

- Firstly, the equation for light gathering power is needed (
**G**) → Light grasp;_{L}**brightness increase**

- D = objective diameter (mm)
- d = eye pupil diameter (mm)

**brightness increase:** how much more light can telescope gather compared to the human eye

**Brightness increase in the terms of magnitudes:**

## Calculating the limiting magnitude of the telescope for d = 7 mm

The maximum diameter of the **human** pupil is 7 mm.

*The actual value is 4.22, but for easier calculation, value 4 is used. Because of this simplification, there are some deviations on the final results*.

The faintest magnitude our eye can see is magnitude 6. This value has to be added to G_{mag }to get the value of the faintest magnitude that can be seen with a particular telescope (m).

__Example: __

d = 7 mm

__D=500mm__

The faintest magnitude that can be seen with the telescope with the objective diameter 500 mm is 15.49!

## Calculating the limiting magnitude of the telescope for any diameter of the human pupil (without rounding the number down)

__Example: __

d=7mm

__D=500mm__

If we compare the results from the first equation, we can see that there is a small difference in the final result. But as I stated before, this occurs because of rounding the number down.

In most cases, the first equation is used (m=2+5*log(D)). We must take into consideration that this equation doesn’t include:

- the
**light**that is lost within the telescope, **seeing conditions**and- telescope’s
**age**.