Theme 2: The theoretical eye Form and dimensions of the eye Optical constants of the eye Optical Geometry applied to the eye Schematic model of the eye Pupils of the eye

Form and dimensions of the eye Sphere of 12 mm radius. Transparent anterior cap, fragment of a sphere of 8 mm radius. Distance between the centers 5mm.

Form and dimensions of the eye Cornea Pupil Lens (crystalline) Retina Fovea Optical nerve

Form and dimensions of the eye Anterior chamber. Between the cornea and the iris. Contains the aqueous humor. Posterior chamber. Between the iris, the ciliary body, and the crystalline lens. Contains the aqueous humor. Vitreous body. Between the crystalline lens and the retina. Contains the vitreous humor.

Optical constants of the eye cornea (r 1c, r 2c ) crystalline (r 1L, r 2L,....) Thicknesses: Cornea (e c ) Anterior chamber Posterior chamber Crystalline (e h ) Vitreous body Refractive indices: Cornea (n C ) Aqueous humor (n ha ) Crystalline (n L ) Vitreous humor (n hv ) The radii of the surfaces’ curvature:

Vergences Vergence: refractive index divided by the distance x’>0 X’>0 convergence x<0 X<0 divergence Unit Diopters Geometric optics applied to the eye

Power of an optical system: Vergence of the image focal distance Power of a spherical dioptric: Vergences Geometric optics applied to the eye

Relationships of conjugation (origin of principal planes. Gauss equation) Vergences Geometric optics applied to the eye

Power of a dioptric The joining of two optical systems n1n1 n 1 ’=n 2 n2’n2’

Geometric optics applied to the eye Cardinal elements n1n1 n 1 ’=n 2 n2’n2’ H 1 =H 1 ’H 2 =H 2 ’ F1F1 F’ 1 F’ 2 F2F2 f1f1 f’ 1 f2f2 f’ 2 Principal planes and points

Geometric optics applied to the eye Cardinal elements n1n1 n 1 ’=n 2 n2’n2’ H FF’ f f’ H Focal planes and points

Schematic model of the eye Procedure in order to obtain a schematic model Geometric representation of the cornea. Geometric representation of the crystalline. Geometric representation of the complete eye. (Association cornea and crystalline). Obtaining the pupils. “Representation of the eye as an optical system working in the paraxial zone within the frame of geometric optics.” Schematic model of the eye:

Cornea ParametersValue Thickness0.55 mm Radius of the first surface 7.8 mm Radius of the second surface 6.5 mm Air index1 Cornea index Aqueous humor index Schematic model of the eye Le Grand model The cornea: Geometric representation

Power Power of the first surface Power of the second suface Schematic model of the eye The cornea: Geometric representation

Power Joining distance Total power of the cornea Schematic model of the eye The cornea: Geometric representation

Cardinal elements Principal planes and points Schematic model of the eye The cornea: Geometric representation

Cardinal elements Focal distances Schematic model of the eye The cornea: Geometric representation

Simplified cornea The principal planes are very close. Thus, the cornea can approximate to just one surface Schematic model of the eye The cornea: Geometric representation

The crystalline: Geometric representation Crystalline parametersValues Thickness4 mm Radius of the first surface 10.2 mm Radius of the second surface -6 mm Aqueous humor index Crystalline index1.42 Vitreous humor index1.336 Schematic model of the eye Le Grand model

Schematic model of the eye Power Power of the first surface Power of the second surface The crystalline: Geometric representation

Schematic model of the eye Power Joining distance Total power of the crystalline The crystalline: Geometric representation

Cardinal elements Principal points and planes Schematic model of the eye The crystalline: Geometric representation

Cardinal elements Focal distances Schematic model of the eye The crystalline: Geometric representation

The complete eye: Geometric representation Joining distance Schematic model of the eye Total power of the eye Power

Cardinal elements Principal points and planes Schematic model of the eye The complete eye: Geometric representation

Cardinal elements Focal distances Schematic model of the eye The complete eye: Geometric representation

Schematic model of the eye Reduced schematic model (Listing) Eye: 1 dioptric SH o =1.59 mm  1.75mm SH’ o =1.91 mm  1.75mm The complete eye: Geometric representation

The pupils of the eye The aperture of the diaphragm (DA) of an optical system is the orifice that limits the extention of the beam of light that penetrates it coming from an object point. The DA limits the passage of light through the system. The iris is the diaphragm of the eye.

Entrance pupil Entrance pupil: Image of the iris through the cornea Optical system to keep in mind: Cornea The pupils of the eye The method of calculation that we will use consists in obtaining the anti-image of the iris through the cornea.

Position Entrance pupil The pupils of the eye Size

The pupils of the eye Position Exit pupil Exit pupil: image of the iris through the crystalline Optical system to keep in mind: Crystalline Size

The pupils of the eye Exit pupil Entrance pupil: 0.56 mm in front of the iris, 13% greater Exit pupil: 0.08 mm behind the iris, 4% greater