Focusing near and far

Look at your finger. Then look at the far wall. Both look sharp.

Tap each distance. Watch the lens. Try 10 cm.

The rule

The eye keeps both sharp by changing its lens. The retina cannot move. The image distance is the gap from lens to retina. So the image distance stays the same. Focal length is how far from the lens parallel rays meet. The lens changes its focal length instead. This is accommodation.

The eye lens changes shape to focus. Ciliary muscles relax for far objects and contract for near ones. The nearest sharp distance is the near point, about 25 cm. A thick lens bends light more. So its focal length is shorter.

The near point is the nearest sharp distance. The far point of a normal eye is infinity. Infinity here means very far away. Closer than 25 cm, even the thickest lens cannot focus.

In a simple model, the retina is 2.3 cm behind one lens. Three letters name distances from the lens:

• u: the object distance.
• v: the image distance.
• f: the focal length.

A distance on the object's side is negative. The lens formula is 1/f = 1/v − 1/u.

A far object has 1/u = 0. So 1/f = 1/v, and f = v = 2.3 cm.

An object at 25 cm has u = −25 cm. The retina is still at v = 2.3 cm.

• 1/f = 1/2.3 − 1/(−25)
• 1/f = 1/2.3 + 1/25
• 1/f = 0.435 + 0.04 = 0.475
• f = 1 ÷ 0.475 = 2.11 cm

So 2.11 cm is about the shortest f a normal lens reaches.

Try the lab to finish this lesson.