A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should. (Select the best option)

We need to determine what improves the resolving power of a compound microscope.

The resolving power formula:

The resolving power (RP) of a microscope is given by:

$$RP = \frac{2\mu \sin\theta}{\lambda}$$

where:

- $$\mu$$ is the refractive index of the medium between the object and the objective lens

- $$\theta$$ is the half-angle of the maximum cone of light entering the objective

- $$\lambda$$ is the wavelength of light used

The term $$\mu \sin\theta$$ is called the numerical aperture (NA) of the objective lens.

Analyzing each option:

Option A: Increase the wavelength of light — From the formula, RP is inversely proportional to $$\lambda$$. Increasing wavelength would decrease the resolving power. This is incorrect.

Option B: Increase the refractive index of the medium between the object and objective lens — From the formula, RP is directly proportional to $$\mu$$. Increasing $$\mu$$ (for example, by using oil immersion instead of air) would increase the resolving power. This is correct.

Option C: Decrease the focal length of the eyepiece — The focal length of the eyepiece affects the magnifying power of the microscope, not its resolving power. Resolving power depends on the objective lens and the medium, not the eyepiece. This is incorrect.

Option D: Decrease the diameter of the objective lens — A smaller objective lens aperture would reduce $$\sin\theta$$, thereby decreasing the resolving power. This is incorrect.

The correct answer is Option B: Increase the refractive index of the medium between the object and objective lens.