Answer
Oil provides better resolution
Work Step by Step
Resolution= 0.61/n, n= refractive index of the medium
Refractive index of air= 1, Refractive index of oil= 1.4
Resolution with oil= 0.61/1.4= 0.435 um
Resolution with air= 0.61/1= 0.61 um
0.61$\gt$0.435
Oil provides better resolution.