The question asks about the effect of immersing a spherical mirror in a liquid on its focal length. We need to understand how the surrounding medium affects the focal length of a spherical mirror. Let's go through the concepts step-by-step:

1. Nature of Focal Length: The focal length of a mirror is determined by its shape and the refractive index of the medium surrounding it. For spherical mirrors, the focal length is given by the formula:

\(f = \frac{R}{2}\)

where \(R\) is the radius of curvature of the mirror. This formula assumes that the mirror is in air or vacuum.

1. Effect of Immersion: When a mirror is immersed in a liquid, the refractive index of the surrounding medium changes. The focal length of a mirror primarily depends on the geometry of the mirror and is less affected by the outside medium compared to lenses.
2. Specular Reflection: The mirror continues to obey the law of reflection (angle of incidence = angle of reflection) irrespective of the surrounding medium. Hence, for mirrors, the focal length remains the same as it is geometrical in nature and does not depend on the medium.
3. Correct Answer: Due to immersion, the only effect on the focal length comes from the change in speed of light in the medium if refraction were considered, but mirrors only reflect. Hence, the focal length remains unchanged. However, given the options, it's implied that it might “depend on the nature of the liquid” in some indirect context or refers to adaptations when mirror-lens systems are discussed. Nevertheless, technically, focal length of a mirror remains unchanged due to its non-dependence on the medium.

Therefore, if we take a broader understanding of the context provided in the options, technically speaking, the focal length remains unchanged, but it may imply dependency due to varied interpretations.