Move the candle along the bench and watch the ciliary muscle reshape the lens so the rays focus on the retina. Change age, eyeball length and glasses to see myopia, hyperopia and presbyopia - and what the prescription fixes.
-accommodation used / available
-total power of the eye + glasses
-defocus (power - power needed)
-blur circle on the retina
-range of sharp vision
-lens thickness
The science
Vergence. Light from an object at distance d reaches the eye with vergence U = -1/d (dioptres, metres). The eye adds its power P and the light converges to an image at distance v inside the vitreous (refractive index n = 1.336): n/v = P - 1/d. The image is sharp when v equals the axial length L, so the power needed is P_req = n/L + 1/d. A relaxed normal eye has P = 60 D, so L = n/P = 22.3 mm.
Accommodation. The ciliary muscle contracts, the zonule fibres slacken and the elastic lens rounds up and thickens, adding A dioptres: P = 60 + S + A, where S is the spectacle power (thin lens at the cornea). The eye uses A = P_req - 60 - S, limited to 0 ... A_max. A_max falls with age; the Hofstetter mean is A_max = 18.5 - 0.30 age (typical value, individuals vary by about 2 D). The nearest sharp object (near point) is therefore at about 1/A_max.
Blur. If the power is wrong by dP = P - P_req, the rays from the two edges of a pupil of diameter D_p meet at a different distance than the retina, and a point becomes a disc of diameter b = D_p L |dP| / n (exact in this model). The small view shows letters spread with that disc (5 arcmin letters = 20/20 size). The eye accepts about 0.25 D either way (depth of focus) before it looks blurred - the sharp-image test used here.
Eye length and glasses. Myopia (long eye, L > 22.3 mm): the image forms in front of the retina, a concave lens S = n/L - 60 (negative) corrects it; each extra millimetre needs about -2.7 D. Hyperopia (short eye): the image is behind the retina; the young eye hides it by accommodating, which tires the muscle at near work. Presbyopia: A_max falls to about 1 D by 60, so a plus lens (reading glasses) takes over part of the near power.
Simplifications. A reduced eye: all refraction at one principal plane (0 mm) into one medium; no spherical aberration, astigmatism, chromatic effects or Stiles-Crawford effect. The drawn eye is a schematic cross-section, the object distance on the bench uses a compressed (logarithmic) scale, and the candle is not to scale. Lens thickness (3.6 mm + 0.06 mm per dioptre), the 0.25 D depth of focus and Hofstetter's amplitude are typical values, not measurements of a person.