JEE Main & Advanced Physics Ray Optics Resolving Limit and Resolving Power

(1) Microscope : In reference to a microscope, the minimum distance between two lines at which they are just distinct is called Resolving limit (RL) and it?s reciprocal is called Resolving power (RP)

\[R.L.=\frac{\lambda }{2\mu \sin \theta }\] and\[R.P.=\frac{2\mu \sin \theta }{\lambda }\Rightarrow \]\[R.P.\propto \frac{1}{\lambda }\]

\[\lambda =\] Wavelength of light used to illuminate the object,

\[\mu =\] Refractive index of the medium between object and objective,

\[\theta =\] Half angle of the cone of light from the point object, \[\mu \sin \theta \]= Numerical aperture.

(2) Telescope : Smallest angular separations \[(d\theta )\] between two distant objects, whose images are separated in the telescope is called resolving limit. So resolving limit \[d\theta =\frac{1.22\lambda }{a}\]

and  resolving power \[(RP)=\frac{1}{d\theta }=\frac{a}{1.22\lambda }\Rightarrow \]\[R.P.\propto \frac{1}{\lambda }\] where a = aperture of objective.