Here's the explanation:

The length of a Galilean telescope is equal to the difference between the focal lengths of its objective lens and its diverging eyepiece.

Here's why:

* Objective Lens: The objective lens is the larger lens at the front of the telescope. It gathers light and forms a real image of the distant object.

* Eyepiece: The eyepiece is the smaller lens you look through. It is a diverging lens (concave) which acts as a magnifying glass to enlarge the real image formed by the objective lens.

Formula:

* Length = Focal Length of Objective Lens - Focal Length of Eyepiece

Example:

Let's say:

* Objective Lens Focal Length = 100 mm

* Eyepiece Focal Length = -25 mm (negative because it's a diverging lens)

Then, the length of the Galilean telescope would be:

* Length = 100 mm - (-25 mm) = 125 mm

Important Considerations:

* The length of a Galilean telescope is significantly shorter than a traditional refracting telescope (which uses a converging lens for its eyepiece).

* Galilean telescopes have a limited magnification and a narrow field of view.

* They are typically used in low-power applications like opera glasses or finding objects in the sky.

I hope this explanation helps!