What is the minimum length to which the focal length of our eye can go, even when considering the blurred images too.
The focal length of the average, healthy, adult human eye at near-point is about 18.5 mm. Young individuals can accommodate their lenses further to a focal length of around 15.4 mm.
The focal length of the human eye is the distance between the lens and the retina when an object is in focus (Fig. 1). Therefore, the
...even when considering blurred images too part in the question doesn't make much sense. So, I will focus my answer on sharp images only (pun intended).
The lenses of the eye are thicker in the center than at the edges, and hence positive and converging lenses. They form an inverted image on the photosensitive layer in the back of the eye - the retina (Fig. 1) The retinal image is shaped by two lenses: 1) the cornea with a fixed focal length and 2) the eye-lens, which is a lens with variable focal length through shape changes (Fig. 1) called accommodation and is mediated by the ciliary muscles (Kolb, 2012).
When the ciliary muscles are relaxed, the focal length of the eye-lens is maximal and the distant objects are in focus (infinity). When the ciliary muscles contract they shorten the focal length of the eye-lens to bring nearer objects into focus. The two limits of this range are called the far-point, (ciliary muscles relaxed), and the near-point (maximal accommodation) (source: University of Colorado, Boulder).
The distance between the eye-lens and the retina is about 20 mm. When an object is far away from the eye (infinity), the image is located essentially at the focal point. Therefore the focal length of the cornea and the eye-lens should be about 20 mm when the muscles of the eye are relaxed. The lens strength is the reciprocal of its focal length in meters. Hence, the strength of the cornea and the eye-lens at the far-point is about 1/0.020 = 50 diopters (source: University of Colorado, Boulder)..
When an object is located at the near-point (the closest point at which an object can be brought into clear focus on the retina), the focal length of the cornea and the eye-lens must be changed so that the image is formed on the retina, which is still 20 mm away. The typical near-point in an adult is 25 cm, corresponding to a focal length of the cornea and the eye-lens of 18.52 mm using the standard ray-tracing rules of lenses. Hence the strength of the cornea and the eye-lens must now be about 1/0.01852 = 54 diopters. In other words, the muscles of the eye can provide an accommodation range of 4 diopters (source: University of Colorado, Boulder).
Kids can, however focus to points as close as 6.5 cm away, i.e., 15 diopters worth of optical power, i.e., a minimal focal length of 15.39 mm.
Fig. 1. Human eye. Upper panel: non-accomodated relaxed eye. Lower panel: accomodated eye. source: Khan Academy