In a simple microscope, the lens is held at a distance d from the eye and the image is formed at the least distance (D) of distinct vision from the eye. What is the magnifying power of the microscope?

The magnifying power (M) of a simple microscope is defined as the ratio of the angle subtended by the image at the eye to the angle subtended by the object when placed at the least distance of distinct vision (D) [t2][t3]. When the lens is held at a distance 'd' from the eye and the image is formed at the near point 'D' from the eye, the image distance from the lens (v) becomes (D - d). Using the lens formula 1/v - 1/u = 1/f [c1], and substituting v = -(D - d) (using sign convention), we find the object distance u. The magnifying power is given by M = D/u. Substituting the derived value of u into this ratio yields the expression M = 1 + (D - d)/f. If the lens is held close to the eye (d = 0), the formula simplifies to the standard 1 + D/f [t1][t6].

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction > 9.3.7 Lens Formula and Magnification > p. 155