The ratio of resolving powers of an optical microscope for two wavelengths ${\lambda }_1=4000\text{A˚}$ and ${\lambda }_2=6000\text{A˚}$ is:

The resolving power (RP) of an optical microscope is inversely proportional to the wavelength of light used:
$$\text{RP}\propto \frac{1}{\lambda }$$
Therefore, the ratio of resolving powers is:
$$\frac{{\text{RP}}_1}{{\text{RP}}_2}=\frac{{\lambda }_2}{{\lambda }_1}=\frac{6000}{4000}=\frac{3}{2}$$