Two telescopes of different length produce the same angular...

Name: Problem 66, Chapter 27: Physics
Uploaded: 2021-03-29T11:43:56-08:00
Duration: 2 min 37 s
Channel: Khoobchandra Agrawal
Description: Two telescopes of different length produce the same angular magnification. Is the focal length of the long telescope's eyepiece greater than or less than the focal length of the short telescope's eyepiece? Explain.

Two telescopes of different length produce the same angular magnification. Is the focal length of the long telescope's eyepiece greater than or less than the focal length of the short telescope's eyepiece? Explain.

Key Concepts

Angular Magnification

Angular magnification is the ratio of the focal length of the objective lens to that of the eyepiece. It determines how much larger an object appears when viewed through a telescope. This ratio is independent of the physical size of the telescope, meaning that different telescopes can have the same angular magnification if the ratio of their focal lengths is maintained.

Relationship Between Focal Lengths of Objective and Eyepiece

In a telescope, the angular magnification is defined as the objective’s focal length divided by the eyepiece’s focal length. When two telescopes produce the same angular magnification, any change in the objective’s focal length must be matched by a proportional change in the eyepiece’s focal length. Thus, if one telescope is physically longer because it has a longer objective focal length, its eyepiece must also have a longer focal length to preserve the same magnification ratio.

Telescope Length Considerations

The overall length of a telescope (in a simple design) is roughly the sum of the focal lengths of the objective and the eyepiece. Therefore, when comparing two telescopes with the same magnification, the longer telescope has a proportionately longer objective focal length, which in turn means its eyepiece focal length is increased by the same factor. This explanation underlines how design adjustments maintain constant magnification while altering the instrument's size.

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