3.9: The Telescope

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A telescope enlarges the retinal image of a distant object. Like a compound microscope, it is also composed of an objective and an eyepiece as seen in Figure \(\PageIndex{1}\). The object in this figure is at a large but finite distance; therefore, an image is formed by the objective just after its second focal point. The eyepiece makes a virtual magnified image, to be viewed with a relaxed eye. Therefore, the intermediary image of the objective must be within the focal length \(f_{i}^{e}\) from the eyepiece. The final image is inverted.

3.8.1.jpg — Figure \(\PageIndex{1}\): Keplerian astronomical telescope.

As seen earlier, the angular magnification is: \(\mathrm{MP}=\alpha_{a} / \alpha_{u}\) where \(\alpha_{u}\) is the half angle of the cone of light that would be collected without telescope and \(\alpha_{a}\) is the half angle of the apparent cone of rays coming from the virtual image of the eye piece. From triangles \(F_{o}^{o b j} B C\) and \(F_{i}^{e} D E\) in Figure \(\PageIndex{1}\) we see that \[\mathrm{MP}=-\frac{f_{i}^{o b j} \mid}{f_{i}^{e}} \nonumber \]

3.8.2.jpg — Figure \(\PageIndex{2}\): Ray angles for a telescope