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

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

Yuu 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

Converging Lenses

Converging lenses are optical components that focus parallel incoming light rays to a focal point. Their design is based on having positive focal lengths, and they serve as the main components in instruments like telescopes by gathering and converging light to form images.

Angular Magnification

Angular magnification refers to the ratio by which an optical instrument enlarges the apparent size of an object. In telescopes, it is calculated by dividing the focal length of the objective lens by the focal length of the eyepiece, indicating how many times larger the object appears compared to the naked eye.

Objective and Eyepiece

In a telescope, the objective lens is responsible for collecting light and forming a real image from a distant object, while the eyepiece lens magnifies that image for viewing. The roles of these lenses are fundamental for the overall optical design and directly affect the magnifying power and clarity of the telescope.

Lens Selection for Maximum Magnification

To maximize angular magnification in a telescope, one should select an objective lens with the longest available focal length to collect more light and form a larger real image, and an eyepiece with the shortest focal length to achieve greater magnification. This combination maximizes the ratio of focal lengths, thereby increasing the telescope’s overall power.

Telescope Configuration and Image Formation

The proper configuration of a telescope requires that the distance between the objective and eyepiece lenses is approximately equal to the sum of their focal lengths. This ensures that the image formed by the objective lens falls exactly at the focal point of the eyepiece, allowing for a relaxed and clear viewing experience when observing distant objects.

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