What is the length of a 2.5x Galilean telescope focused for infinity with a -25D ocular lens?

To determine the length of a 2.5x Galilean telescope focused for infinity with a -25D ocular lens, it's essential to understand the components of a Galilean telescope. This type of telescope consists of a converging objective lens and a diverging ocular lens. The magnification (M) of a Galilean telescope is given by the formula M = -f_objective / f_ocular, where f represents the focal lengths of the respective lenses.

In this case, the ocular lens has a power of -25 diopters. To find its focal length, we can use the formula:

f_ocular = 1 / power = 1 / -25 = -0.04 m = -4 cm.

Given that the telescope has a magnification of 2.5x, we can rearrange the magnification formula to find the focal length of the objective lens:

2.5 = -f_objective / (-4 cm)

=> f_objective = 2.5 * (-4 cm) = 10 cm.

Now, the length of a Galilean telescope when focused for infinity is the sum of the absolute values of the focal lengths of the two lenses:

Length = |f_objective| +