A person has an eye-lens whose maximum focal length exceeds its...

By the lens formula for the human eye, we have $\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$, where $v$ is the distance of the retina from the eye-lens, $u$ is the object distance, and $f$ is the focal length.

For any real object at a distance $x$ from the eye, $u = -x$ ($x > 0$). Substituting this into the lens formula gives:

$\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{x}$

Since $x > 0$, it follows that $\dfrac{1}{f} > \dfrac{1}{v}$, which implies $f < v$. This means that to clearly see any real object, the required focal length of the eye-lens must be strictly less than the distance to the retina.

The eye is in its relaxed (unstrained) state only when its focal length is at its maximum value, f_\max.

The problem states that f_\max > v. However, seeing any object requires $f < v$. Since f < v < f_\max, the eye can never use its maximum focal length to view a real object. The ciliary muscles must always contract to decrease the focal length from f_\max to the required value $f$.

Therefore, the eye is always strained while looking at an object.