Resolving Power of Microscope

The resolving power of a microscope depends not just on its ability to magnify, but on its ability to resolve two points on the object separated by a small distance $d_{\min}$ -- the smaller $d_{\min}$, the better the resolving power. Mapping the image-plane Airy-disc radius $r_0=1.22f\lambda/a$ (from Rayleigh's criterion) back to the object plane, using the half-angle $\beta$ the objective's aperture subtends at the object (via $\tan\beta\approx\sin\beta=a/f$), gives $\boxed{d_{\min}=\dfrac{1.22\lambda}{2\sin\beta}}$. To reduce $d_{\min}$ further, the objective can be immersed in a bath of oil of refractive index $n$, giving $d_{\min}=\dfrac{1.22\lambda}{2n\sin\beta}$; such an objective is called an oil-immersion objecti …