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• The lecture covers the physics of eyes and vision. Topics include the visual system, eye elements, focusing elements, sensitivity, image formation on the retina, and vision defects.

Visual System

• The sense of vision consists of:
  • The eyes, which focus an image from the outside world onto the light-sensitive retina.
  • Millions of nerves that carry the information deep into the brain.
  • The visual cortex, a part of the brain where everything is put together.
• Blindness results if any of these parts do not function.

Vision Elements of the Eye

• The cornea is the clear, transparent bump on the front of the eye that is responsible for about two-thirds of the eye's focusing power.
• The eye has two major focusing components: the cornea (fixed focus element) and the lens (variable shape).

Focusing Elements of the Eye

• The cornea focuses light by bending (refracting) light rays.
• The amount of bending depends on the curvature of the corneal surfaces and the speed of light in the lens relative to the surrounding material.
• The index of refraction is nearly constant for all corneas, but curvature varies considerably from person to person, causing defective vision.
• Indexes of Refraction:
  • Cornea: 1.37
  • Aqueous humor: 1.33
  • Lens cover: 1.38
  • Lens center: 1.41
  • Vitreous humor: 1.33

Vision Elements: Iris and Pupil

• The iris is the colored part of the front eye, adapting vision from light to dark and vice versa. It adjusts incident light on the retina until the retina adapts to the new lighting. It also reduces lens defects under bright light.
• The pupil is the small opening in the center of the iris where light enters the lens.
• The pupil appears black because almost all the light that enters is absorbed inside the eye.
• Under average light conditions, the opening is approximately 4mm.
• It can change from approximately 3mm in diameter in bright light to 8mm in diameter in dim light.

Vision Elements: Lens

• The lens is variable in shape, focusing objects at various distances using both its front and back surfaces.
• It is more curved in the back than in the front.
• The focusing power of the lens is less than that of the cornea (1/3) because of surrounding substances with nearby refraction indexes.
• The lens comprises layers resembling an onion, but not all layers have the same refractive index (n).

Vision Elements: Aqueous Humor

• The aqueous humor fills the space between the lens and the cornea and mostly waters (n ≈ 1.33).
• It is continuously produced, and the surplus escapes via the "Canal of Schlemm."
• Blockage of these drain tubes results in increased eye pressure, leading to "Glaucoma."
• Maintains internal eye pressure at about 20mm Hg.
• It contains many blood components and supplies nutrients to the non-vascularized cornea and lens.

Vision Elements: Vitreous Humor and Sclera

• The vitreous humor is a clear, jelly-like substance filling the large space between the lens and the retina, which helps maintain the eye's shape and is essentially permanent.
• The sclera is the tough, white, tight covering over the eye, except for the cornea, and is protected by a transparent coating called the conjunctiva.

Vision Elements: Retina

• The retina is the eye's light-sensitive part, converting light images into electrical nerve impulses sent to the brain.

Sensitivity of the Eye and Image Formation on the Retina

• The retina (the eye's light detector) converts light images into electrical nerve impulses sent to the brain. A light photon's absorption in a photoreceptor causes a photochemical reaction, initiating an action potential and then producing electrical nerve impulses sent to the brain.
• Most vision is restricted to the macula lutea (yellow spot).
• Detailed vision occurs in the fovea centralis (0.3mm diameter) within the yellow spot.

Eye Photoreceptors

• There are two types of photoreceptors in the retina: cones and rods. They are distributed symmetrically in all directions from the visual axis, except in the blind spot.
• Blind Spot has neither rods nor cones. It is a region from about 13º to 18º.
• Cones: 6.5 million in each eye, used for daylight vision and recognizing different colors, primarily found in the fovea centralis, and each has its own nervous link to the brain. Density determines the amount of detail we can resolve. Maximum sensitivity is around 550 nm in the yellow-green region.

Rods vs Cones

• Rods: 120 million in each eye, used for night vision and peripheral vision, covering most of the retina, with a maximum density at about 20° the vision axis. Hundreds of rods send their information to the same nerve fiber. They are most sensitive to blue-green light (~510nm) and continue to dark-adapt for 30 to 60 minutes.

Image Formation on the Retina

• Near Objects:
  • Eye muscles taut, muscle fibers shorten, and the eye lens becomes thicker and more powerful.
• Far Objects:
  • Eye muscles relax, muscle fibers lengthen, and the eye lens becomes thinner and less powerful.

Near and Far Points

• Normal Vision:
  • Typical near point is 25cm.
  • Typical far point is infinity (∞).
• At near point: 1/f = 1/0.25 + 1/0.02 = 4 + 50 = 54 m⁻¹
• At far point: 1/f = 1/∞ + 1/0.02 = 0 + 50 = 50 m⁻¹

Accommodation

• Accommodation
  • The strength of the eye lens can be expressed in term of the optical power (P), where P(diopter) = 1/f(m)
  • The power of the convex (convergence) lens is positive, and the power of the concave (divergence) lens is negative.
• For normal vision:
  • At near point: P = 1/0.25 + 1/0.02 = 54 m⁻¹ = 54D
  • At far point: P = 1/∞ + 1/0.02 = 50 m⁻¹ = 50D
  • Paccomm = [P]near - [P]far = [1/do + 1/di]near - [1/do + 1/di]far

Diopter Strength of the Eye

• The focal length F of a combination of two lenses with focal lengths F1 and F2 is given by: 1/F = 1/F1 + 1/F2 + ... + 1/Fn
• If Lens A with focal length F = 0.33m is combined with Lens B (focal length = 0.25m): 1/F = 1/0.33 + 1/0.25 = 3 + 4 = 7 D

Vision Defects

• Nearsightedness(Myopia): the ability to see near objects clearly, while distant objects appear burry
  • Due to the too strong eyelens or too long eye ball.
  • The eye over converges the nearly parallel rays from a distant object, and the rays cross in front of the retina.
• Vision comes with a Myopia Correction which requires placing diverging eyeglass (concave) lens in front of the eye.

Farsightedness (Hyperopia)

• The ability to see far objects clearly, and distant objects are blurry.
• Due to the too weak eye lens or too short eye ball.
• A farsighted does not sufficiently converge the rays from a near object to make the rays meet on the retina.
• To correct, place a converging eyeglass (convex) lens in front of the eyes.

Presbyopia

• The loss of the eye's ability to change its focus to see objects that are near.
• Part of the natural aging process and easily corrected. Commonly occurs at 45 year of age.
• Corrected with bifocal lenses.

Bifocal Lenses

• Consists of both concave and convex lenses.
  • The upper portion consists of a concave lens to facilitate distant vision.
  • The lower part is a convex lens to facilitate near vision.

Astigmatism

• When present, point objects do not from clear point images on the retina, normally due to the corneas having unequal curvature in different directions.
• Astigmatism is corrected with asymmetric lenses.

Equation for Vision Defects

• The equation to find and calculate the power of the glass needed to correct any type of vision defect: Pnormal = Ppatient + Pglass

Example Calculation of Vision Correction

• A strength and the focal length of a lens is need to correct a myopic eye at a far point of 1m. $ Pnormal = \frac{1}{fnormal} = \frac{1}{d_0} + \frac{1}{d_i} $ becomes $ Pnormal = \frac{1}{\infty} + \frac{1}{0.02} = 0 + 50 = 50D $ $ Ppatient = \frac{1}{fpatient} = \frac{1}{d_0} + \frac{1}{d_i} $ becomes $ Pnormal = \frac{1}{1} + \frac{1}{0.02} = 1 + 50 = 51D $ $ Pglass = Pnormal + Ppatient = 50 - 51 = -1D $ (negative = concave lens)