1. For an optical instrument, the resolving power is inversely proportional to the wavelength:

$R \propto \frac{1}{\lambda}$

So for two wavelengths $\lambda_1$ and $\lambda_2$,

$\frac{R_1}{R_2} = \frac{\lambda_2}{\lambda_1}$

2. Given:

$\lambda_1 = 4000\,\text{\AA}, \qquad \lambda_2 = 5000\,\text{\AA}$

Therefore,

$\frac{R_1}{R_2} = \frac{5000}{4000} = \frac{5}{4}$

3. Hence the ratio of resolving powers corresponding to $\lambda_1$ and $\lambda_2$ is

$R_1 : R_2 = 5:4$

4. Checking options:

• A: $16:25$ ❌
• B: $9:1$ ❌
• C: $4:5$ ❌
• D: $5:4$ ✅

Therefore, the correct option is D.