An amateur astronomer wants to build a small refracting...

An amateur astronomer wants to build a small refracting telescope. The only lenses available to him have focal lengths of $5.00 \mathrm{cm}, 10.0 \mathrm{cm}, 20.0 \mathrm{cm},$ and 30.0 $\mathrm{cm} .$ (a) What is the greatest magnification that can be obtained using two of these lenses? (b) How long is the telescope with the greatest magnification?

An amateur astronomer wants to build a small refracting telescope. The only lenses available to him have focal lengths of $5.00 \mathrm{cm}, 10.0 \mathrm{cm}, 20.0 \mathrm{cm},$ and 30.0 $\mathrm{cm} .$ (a) What is the greatest magnification that can be obtained using two of these lenses?
(b) How long is the telescope with the greatest magnification?

Key Concepts

Lens Combination in Optical Instruments

Combining lenses with different focal lengths allows for the customization of the telescope's magnification and physical dimensions. Choosing appropriate lenses is critical for optimizing performance, as it involves balancing magnification with practical considerations such as the overall length and clarity of the image.

Optical Tube Length

The optical tube length of a refracting telescope is typically the sum of the focal lengths of the objective and the eyepiece lenses. This length is important because it determines the physical size of the telescope and affects its portability and ease of use.

Magnification

Magnification in telescopes is the ratio of the focal length of the objective lens to that of the eyepiece lens. A higher magnification is achieved by using an objective with a long focal length paired with an eyepiece with a short focal length, which enlarges the perceived size of distant objects.

Refracting Telescope

A refracting telescope is an optical instrument that uses a system of lenses to form images, typically consisting of an objective lens that gathers light and an eyepiece lens that magnifies the image formed by the objective. It is one of the simplest types of telescopes and serves as a foundation for understanding more complex optical devices.

Focal Length

Focal length is a measure of how strongly an optical system converges or diverges light, defined as the distance from the lens where parallel light rays converge to a point. In telescopes, the focal lengths of the lenses are key parameters that determine both the magnification and the overall size of the instrument.

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