The part of the eye responsible for fine-tuning the refraction of incoming light is the lens retina optic nerve cornea

The answer is the lens.

The eyeball is filled with a water-like fluid. In front of the eyeball, there is the cornea. It is a transparent structure that refracts light. A portion of light passes through the pupil which allows light to enter the eye. The amount of light that will pass through the pupil depends on dilatation of iris. Once the light enters the eye, it enters the lens. Lens of the eye is able to change its size and that way is responsible for fine-tuning the refraction of the light. The light later reaches the retina.

Cis your correct answer