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How do telephoto attachments and wide-angle attachments change image scale?

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Diagram showing the negative-positive photographic process: a scene is captured on film in a camera, developed into a negative, projected onto paper with an enlarger, and developed again to produce a positive print. — technology of photography Figure 1: Sequence of negative–positive process, from the photographing of the original scene to enlarged print (see text).

In the context of photography technology, afocal attachments modify the image scale produced by a fixed camera lens by acting as magnifying or reducing telescopes.1

Telephoto attachments: These function as magnifying telescopes. A telephoto attachment with a specific magnification factor, such as 1.5×, increases the image scale on the film by that factor.1
Wide-angle attachments: These act as reducing telescopes. A wide-angle attachment with a factor such as 0.7× reduces the image scale to 0.7 times that of the prime camera lens.1

Because these attachments are afocal, they do not have a focal length themselves; instead, they create a virtual image that the camera's prime lens then projects onto the film.1