A 2.5x Galilean telescope with a -25D ocular lens has what length when focused for infinity?

To determine the length of a Galilean telescope focused for infinity, it's essential to understand the configuration and focal lengths involved in a Galilean design. A Galilean telescope consists of a convex objective lens and a concave ocular (eyepiece) lens.

In this scenario, the ocular lens has a power of -25 diopters, which indicates that it is a concave lens. The focal length (f) of a lens can be calculated using the formula ( f = \frac{1}{P} ), where P is the power in diopters. Therefore, the focal length of the ocular lens is:

[ f = \frac{1}{-25} = -0.04 , \text{m} \text{ or } -4 , \text{cm} ]

In a Galilean telescope focused for distant objects (infinity), the setup follows this principle: the rays coming from the distant object converge at the focal point of the objective lens and enter the ocular lens. The length of the telescope (L) that focuses for infinity is the sum of the absolute focal lengths of the objective and ocular lenses.

For a Galilean telescope, the effective length can be expressed as:

[ L =