You have a set of converging lenses with focal lengths 1.00 cm, 10.0 cm, 50.0 cm, and 80.0 cm .

step 1 In this problem, we have a set of four lenses with focal length of 1 ceremitter, 10 ceres, 50 ce

You have a set of converging lenses with focal lengths 1.00...

You have a set of converging lenses with focal lengths $1.00 \mathrm{cm}, 10.0 \mathrm{cm}, 50.0 \mathrm{cm},$ and $80.0 \mathrm{cm} .$ (a) Which two lenses would you select to make a telescope with the largest magnifying power? What is the angular magnification of the telescope when viewing a distant object? (b) Which lens is used as objective and which as eyepiece? (c) What should be the distance between the objective and eyepiece?

Key Concepts

Angular Magnification

Angular magnification in a telescope is the measure of how much larger an object appears compared to viewing it with the naked eye. It is determined by the ratio of the focal length of the objective lens to that of the eyepiece lens, i.e., M = f_objective / f_eyepiece. This ratio increases with a longer objective focal length and a shorter eyepiece focal length, leading to greater magnification of distant objects.

Objective Lens

The objective lens in a telescope is the primary light-collecting element with a long focal length. Its role is to gather light from a distant object and form a real, inverted image at its focal plane. The quality and focal length of the objective lens critically determine the brightness and resolution of the final image.

Eyepiece Lens

The eyepiece lens, or ocular, is used to magnify the image produced by the objective lens. It typically has a short focal length, which, when used in conjunction with the objective lens, sets the angular magnification of the telescope. The observer looks through the eyepiece to see an enlarged version of the object's image.

Focal Length and Lens Separation

Focal length is the distance from a lens to its focus and is crucial in determining the behavior of light passing through the lens. In telescope design, the separation between the objective and eyepiece is ideally set to the sum of their focal lengths, ensuring that the image produced by the objective is exactly at the focal plane of the eyepiece. This alignment allows for an optimal viewing experience with the desired magnification.

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