Simple Microscope

A simple microscope is a single convex lens whose angular magnifying power compares the angle subtended by the image to that subtended by the object at the near point. When the image is formed at the near point $D$, the magnifying power is $M=1+\frac{D}{f}$, the extra unity arising because the eye is fully accommodated. Substituting $D=25$ cm and $f=5$ cm gives $M=1+\frac{25}{5}=1+5=6$. The underlying idea is that magnifying power compares two visual angles: the angle the object would subtend if held at the unaided near point against the larger angle it subtends through the lens. Because a relaxed eye and a fully accommodated eye give slightly different geometries, the near-point formula carries an extra $+1$ that the \infty formula lacks, representing the additional angular gain from bringing the virtual image right up to 25 cm. The value 5 is wrong because it uses $M=\frac{D}{f}$, valid only for relaxed-eye viewing with the image at \infty, not the near point. The value 25 is wrong as it equals $D$ alone and ignores the focal length. The value 1.2 is wrong since it inverts the ratio to $\frac{f}{D}$ plus one. This is the NCERT near-point formula for a magnifier. A plausibility check confirms a short focal length lens yields useful magnification greater than unity, and the near-point value sensibly exceeds the relaxed-eye value by one.