^Resolving power of a compound microscope
Here, λ = wavelength of light used
μ = refractive index of the medium between the object & objective lens
θ = Half angle of the cone of light from each point object.
Also μ sinθ is called numerical aperture.
From above relation it is clear that the resolving power of a compound microscope can be increased by increasing refractive index of the medium. It is due to this reason that oil immersion objectives are used to increase the resolving power. Also, higher the value of numerical aperture, larger will be the resolving power of the microscope.