The distance from the eye-lens to the retina is x . For a normal...

For a normal eye, the maximum focal length of the eye-lens corresponds to the fully relaxed state of the ciliary muscles, which occurs when viewing an object at infinity.

Using the lens formula:

$\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$

Here, the object distance $u = -\infty$ and the image is formed on the retina, so the image distance $v = x$.

Substituting these values into the lens formula:

\dfrac{1}{x} - \dfrac{1}{-\infty} = \dfrac{1}{f_{\text\max}}

\dfrac{1}{x} - 0 = \dfrac{1}{f_{\text\max}}

f_{\text\max} = x

Thus, the maximum focal length of the eye-lens is equal to $x$.