The Eye & Apparent Size

Every optical instrument in this chapter exists to help one remarkable instrument: the eye. Before adding lenses to it, let’s see how it works on its own.

The parts of the eye#

The eyeball is roughly a sphere about 2.5 cm across. Light entering it meets, in order:

• Cornea: the transparent, more sharply curved front window.
• Aqueous humour: a clear liquid behind the cornea.
• Iris and pupil: the iris is the coloured muscular diaphragm; the pupil is the hole in it. The iris widens the pupil in dim light and narrows it in bright light. The pupil looks black because light entering it almost never comes back out.
• Crystalline lens: hard in the middle, softer toward the edge, held by ligaments to the ciliary muscles, which can change its curvature.
• Vitreous humour: the clear jelly filling the space behind the lens.
• Retina: the light-sensitive lining at the back, with about 125 million receptors (rods and cones) and about a million optic-nerve fibres carrying signals to the brain.

Where the bending happens

The two humours have refractive index about 1.336; the lens averages about 1.396. Light entering from air is bent most at the cornea, where the change in refractive index is largest. The lens adds a smaller, adjustable amount. Together, cornea, lens and fluids act like a single converging lens, the eye-lens, whose focal length the ciliary muscles can change.

Accommodation#

Looking at something far away, the ciliary muscles are relaxed and the eye-lens has its longest focal length, equal to its distance from the retina, so parallel rays focus on the retina. For a nearer object the muscles tighten, the lens bulges, and the focal length shortens just enough to keep the image on the retina. This adjustment is called accommodation.

Apparent size#

How big something looks depends on the size of its image on the retina: a bigger image covers more rods and cones. Move an object away and its image shrinks. The image size is roughly proportional to the visual angle, the angle the object subtends at the eye. Optical instruments work by making this angle bigger.