A refracting telescope is used to view the Moon. The focal...

A refracting telescope is used to view the Moon. The focal lengths of the objective and eyepiece are $+2.40 \mathrm{m}$ and $+16.0 \mathrm{cm},$ respectively. (a) What should be the distance between the lenses? (b) What is the diameter of the image produced by the objective? (c) What is the angular magnification?

Key Concepts

Refracting Telescopes

Refracting telescopes use lenses to gather and focus light. The primary element, the objective lens, collects light from a distant object and forms a real image, while the eyepiece acts as a magnifier to produce a virtual image that can be observed by the eye. This basic optical design is central to many astronomical and terrestrial instruments.

Focal Length

The focal length of a lens is the distance from the lens at which parallel incoming light rays converge to a point. In telescopes, the focal lengths of both the objective and the eyepiece determine where the image is formed and influence the overall magnification and size of the image formed by the optical system.

Optical Tube Length (Lens Separation)

For astronomical telescopes designed so that the final image is viewed at infinity, the separation between the objective and the eyepiece lenses is ideally the sum of their respective focal lengths. This ensures that the image produced by the objective is exactly at the focal point of the eyepiece, facilitating relaxed viewing conditions.

Angular Magnification

Angular magnification is a measure of how much larger an instrument makes an object's angular size appear to the observer. In a refracting telescope, it is given by the negative ratio of the focal length of the objective lens to that of the eyepiece lens, which indicates how many times larger an object appears when viewed through the telescope compared to the naked eye.

Image Formation by Lenses

The image produced by a lens is related to the object's angular size and the focal length of the lens. Specifically, for distant objects such as the Moon, the diameter of the image formed by the objective can be determined by multiplying the focal length of the objective by the angular size of the object (in radians). This relationship is key to understanding how telescopes scale down the vast distances and sizes involved in astronomical observations.

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