Astronomical Telescope

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An astronomical telescope in normal adjustment uses an objective of focal length 100 cm and an eyepiece of focal length 5 cm to view distant stars.

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For an astronomical telescope in normal adjustment, NCERT gives the angular magnification as the ratio of the objective focal length to the eyepiece focal length, $M=\frac{f_o}{f_e}$, because the final image is formed at \infty for relaxed viewing. Substituting $f_o=100$ cm and $f_e=5$ cm gives $M=\frac{100}{5}=20$, meaning distant objects appear twenty times larger in angular size. A long objective focal length and a short eyepiece focal length together maximise this magnification, which is why telescope tubes are long. The value 500 is wrong because it multiplies the two focal lengths instead of dividing them. The value 105 is wrong because it adds the focal lengths, which instead gives the approximate tube length in normal adjustment. The value 0.05 is wrong because it inverts the ratio, dividing eyepiece by objective. As stated in NCERT Class 12, Chapter 9, telescope magnification rises with a longer objective and shorter eyepiece focal length. A magnitude check confirms that a metre-long objective paired with a 5 cm eyepiece sensibly yields a twenty-fold angular magnification.

Astronomical Telescope

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