An old refracting telescope in a museum is 45.0 cm long and the caption states that the telesco

step 1 we have better than L equals 45 cm which equals some of the focal length of the objective and th

An old refracting telescope in a museum is 45.0 cm long and...

An old refracting telescope in a museum is $45.0 \mathrm{~cm}$ long and the caption states that the telescope magnifies images by a factor of $30.0$. Assuming these numbers are for viewing an object an infinite distance away with minimum eyestrain, what is the focal length of each of the two lenses?

Key Concepts

Focal Length

Focal length is the distance over which initially collimated (parallel) rays of light are brought to a focus by a lens. It is a fundamental property that determines the converging or diverging power of the lens, and it plays a key role in imaging systems by dictating the size of the image formed relative to the object.

Refracting Telescope Design

A refracting telescope uses a system of two lenses—a large objective lens that collects light and forms an image, and a smaller eyepiece lens that magnifies this image. The overall length of the telescope under relaxed eye conditions is the sum of the focal lengths of these two lenses, enabling comfortable long-duration viewing of distant objects.

Angular Magnification

Angular magnification refers to the factor by which an optical instrument, like a telescope, increases the apparent angular size of an object. In a refracting telescope, it is determined by the ratio of the focal lengths of the objective lens to the eyepiece lens, thus indicating how much larger an object will appear to an observer.

Relaxed Eye Viewing

Relaxed eye viewing implies that the observer’s eye is positioned such that it focuses on an object at infinity, which minimizes eye strain. In telescopic systems, this condition means that the final image formed by the eyepiece is at infinity, and the positioning of the lenses is set to ensure comfortable, prolonged observation.

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