3.9: The Telescope

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.

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

$$\mathrm{MP}=-\frac{f_{i}^{o b j} \mid}{f_{i}^{e}} \nonumber$$

Figure $\PageIndex{2}$: Ray angles for a telescope