**Oil Immersion Objective and Numerical Aperture:**
An oil immersion objective is a specialized lens used in light microscopy that requires the use of immersion oil between the objective lens and the specimen. This oil has a refractive index close to that of glass, which helps to minimize the loss of light due to refraction.

Numerical aperture (NA) is a measure of the light-gathering ability and resolving power of an objective lens. It is determined by the refractive index of the medium between the lens and the specimen, and the angle of the cone of light entering the lens. A higher numerical aperture indicates a greater resolving power of the lens.

**Abbé Equation:**
The Abbé equation is used to calculate the maximum theoretical resolving power (R) of a microscope. It is given by the formula:

R = (0.61 * λ) / NA

Where:
R = Resolving power (in nm)
λ = Wavelength of light used (in nm)
NA = Numerical aperture of the objective lens

**Calculating Resolving Power:**
In this case, we are given that the numerical aperture of the oil immersion objective is 1.25, and the wavelength of the blue light used is 450 nm. We can substitute these values into the Abbé equation to calculate the resolving power:

R = (0.61 * 450) / 1.25
R = 275.4 / 1.25
R ≈ 220.32 nm

Therefore, the maximum theoretical resolving power of the microscope with this oil immersion objective and blue light is approximately 220.32 nm.

**Explanation:**
The resolving power of a microscope determines its ability to distinguish between two closely spaced objects. It is influenced by factors such as the numerical aperture of the objective lens and the wavelength of light used. A higher numerical aperture and a shorter wavelength of light result in a greater resolving power.

In this case, the oil immersion objective has a numerical aperture of 1.25, which is relatively high. The numerical aperture affects the angle of the cone of light entering the lens, allowing for better light-gathering and increased resolving power.

The wavelength of blue light used is 450 nm, which is shorter than the wavelength of visible light. Shorter wavelengths enable higher resolution because the distance between two points that can be distinguished decreases as the wavelength decreases.

By substituting the given values into the Abbé equation, we can calculate the maximum theoretical resolving power of the microscope, which is approximately 220.32 nm. This means that the microscope can distinguish between two points that are at least 220.32 nm apart.

In summary, the oil immersion objective with a numerical aperture of 1.25 and blue light with a wavelength of 450 nm provides a maximum theoretical resolving power of approximately 220.32 nm. This allows for high-resolution imaging and the ability to distinguish fine details in the specimen being observed.