**Core Concept**
The axial length of the eyeball is a crucial factor in determining its refractive power. According to the lens maker's formula, the power of the lens is inversely proportional to the axial length of the eyeball. This means that a change in the axial length will result in a corresponding change in the refractive power of the eye.

**Why the Correct Answer is Right**
The correct answer is based on the lens maker's formula, which states that the power of the lens (P) is equal to (n - 1) / R, where n is the refractive index of the lens material and R is the curvature of the lens. Since the axial length (L) of the eyeball is inversely proportional to the refractive power, a change in L by 1 mm will result in a change in power by (1 / L) * (1 mm). Assuming a typical axial length of 24 mm, this results in a change in power by approximately 0.0417 diopters per millimeter of change in axial length.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because it does not take into account the inverse relationship between axial length and refractive power. A change in axial length will not result in a direct change in power.
* **Option B:** This option is incorrect because it assumes a linear relationship between axial length and refractive power, which is not accurate according to the lens maker's formula.
* **Option C:** This option is incorrect because it does not provide a specific numerical value for the change in power, making it an incomplete and inaccurate answer.

**Clinical Pearl / High-Yield Fact**
A 1 mm change in axial length can result in a significant change in refractive power, highlighting the importance of precise measurements in ophthalmic surgery and refractive correction.

**Correct Answer: D. 0.0417 diopters.**