Astronomical Telescope

In normal adjustment an astronomical telescope is set so that the intermediate image lies at the common focus of both lenses, sending parallel rays to a relaxed eye. Its angular magnifying power is then simply the ratio of focal lengths, $M=\frac{f_o}{f_e}$, where a long objective and a short eyepiece maximise magnification. Substituting $f_o=100$ cm and $f_e=5$ cm gives $M=\frac{100}{5}=20$. The physical picture is that the objective collects nearly parallel rays from a distant star and forms a small real image at its focal plane; positioning the eyepiece so this image sits at its own focus sends parallel rays to the eye, which can then view the magnified image without straining. Magnifying power here is purely angular—stars remain point-like, so it is the apparent angular separation between objects, not their linear size, that the telescope enlarges. The value 25 is wrong because it would require an eyepiece focal length of 4 cm. The value 105 is wrong as it is the tube length $f_o+f_e$ in centimetres, not a magnification. The value 500 is wrong since it multiplies the focal lengths instead of dividing them. This NCERT result explains why research telescopes use very long objective focal lengths. A plausibility check confirms the magnification is dimensionless and exceeds unity because the objective focal length far surpasses that of the eyepiece.