A telescope, consisting of two lenses, has an objective lens...

A telescope, consisting of two lenses, has an objective lens with refractive power $0.186 \mathrm{D}$ and an eyepiece with focal length of $5.33 \mathrm{~cm}$. What is the absolute value of the angular magnification of this telescope?

Key Concepts

Angular Magnification

Angular magnification is the ratio of the angle subtended by the image when viewed through an optical instrument to the angle subtended by the object when viewed with the naked eye. In telescopes, it is calculated by dividing the focal length of the objective lens by the focal length of the eyepiece. This ratio determines how much larger or closer the image appears compared to the actual object.

Unit Conversion

Unit conversion is the process of converting one measure to another to maintain consistency in calculations. In optical problems, such as those involving focal lengths, it is essential to convert all measurements to compatible units (e.g., converting centimeters to meters) to accurately apply formulas like f = 1/D and the calculation of angular magnification.

Refractive Power

Refractive power quantifies how strongly a lens converges or diverges light, and is expressed in diopters (D). It is inversely related to the focal length of the lens (f = 1/D in meters). In telescopes, the refractive power of the objective lens determines its ability to gather light and form a clear image of distant objects.

Focal Length

Focal length is the distance from the lens at which parallel rays of light converge to a point or seem to diverge from a point. It is a crucial parameter in optical instruments like telescopes, affecting both the image brightness and the magnification. For the objective lens, its focal length can be derived from its refractive power, while for the eyepiece, it is a direct measure provided in the problem.

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