\(\mathrm{RP}=\frac{2 \mu \sin \theta}{\lambda}\)
For wavelength \({\lambda _1} = 4000\,\mathop {\text{A}}\limits^o \), resolving power will be
\(\mathrm{RP}_{1}=\frac{2 \mu \sin \theta}{4000}\) ..... \((i)\)
For wavelength \({\lambda _2} = 6000\,\mathop {\text{A}}\limits^o \), resolving power will be
\(\mathrm{RP}_{2}=\frac{2 \mu \sin \theta}{6000}\) ..... \((ii)\)
On dividing eqn. \((i)\) by eqn. \((ii)\)
\(=\frac{\mathrm{RP}_{1}}{\mathrm{RP}_{2}}=\frac{6000}{4000}=\frac{3}{2}\)