A simple magnifying glass (convex lens) has a focal length $f=5\text{cm}$. The near point of the unaided eye is $D=25\text{cm}$. (i) Find the angular magnification $M_{\infty }$ when the eye is relaxed and the final image is at infinity. (ii) Find the angular magnification $M_D$ when the eye is accommodated so that the final image is at the near point $D$.

Step-by-step solution

1. Angular magnification for a relaxed eye (final image at infinity) is $M_{\infty }=\frac{D}{f}$.
2. Substitute $D=25\text{cm}$ and $f=5\text{cm}$: $M_{\infty }=\frac{25}{5}=5$.
3. When the final image is formed at the near point, the magnification is $M_D=1+\frac{D}{f}$.
4. Insert the values: $M_D=1+\frac{25}{5}=1+5=6$.

Concept tested: Magnifying power of a simple lens

Published 14 September 2026 · How this solution was prepared and checked