A refracting telescope has an objective lens of focal length $f_o=80\text{cm}$ and an eyepiece of focal length $f_e=8\text{cm}$. The telescope is adjusted so that the final image is formed at the near point of a relaxed eye ($D=25\text{cm}$). (i) Find the angular magnification $M$ of the telescope in this relaxed‑eye configuration. (ii) If the telescope is instead adjusted for viewing distant stars (final image at infinity), what would be the angular magnification?

Step-by-step solution

1. For a telescope forming the final image at the near point, the angular magnification is $M=-\frac{f_o}{f_e}\left(1+\frac{f_e}{D}\right)$.
2. Substitute $f_o=80\text{cm}$, $f_e=8\text{cm}$, $D=25\text{cm}$: $M=-\frac{80}{8}\left(1+\frac{8}{25}\right)=-10\left(1+0.32\right)=-10\times 1.32=-13.2$, rounded to $-13.0$.
3. For the normal astronomical setting (final image at infinity), the angular magnification simplifies to $M=-\frac{f_o}{f_e}=-\frac{80}{8}=-10$.
4. The negative sign indicates that the image is inverted relative to the object.

Concept tested: Telescope angular magnification

Published 8 September 2026 · How this solution was prepared and checked