Unit X Physical Principles of Optics and Vision and Intraocular Fluid

Physical Principles of Optics

• Optical System of the Eye: Understanding the eye requires knowledge of basic optical principles, including light refraction, focusing, and depth of focus.

• Refractive Index of a Transparent Substance:

  • Light rays travel through air at a velocity of approximately $300,000\,km/sec$.

  • Light travels significantly slower through transparent solids and liquids.

  • The refractive index ($n$) is defined as the ratio of the velocity of light in air ($v_{air}$) to the velocity of light in the substance ($v_{substance}$):         $n = \frac{v_{air}}{v_{substance}}$

  • The refractive index of air is exactly $1.00$.

  • Example: If light travels through glass at $200,000\,km/sec$, the refractive index of that glass is $\frac{300,000}{200,000} = 1.50$.

• Refraction of Light Rays at an Interface:

  • Perpendicular Interface: When light rays strike an interface perpendicular to the beam, they enter the second medium without deviation. Only velocity decreases and wavelength shortens (evidenced by shorter distances between wave fronts).

  • Angulated Interface: If light rays pass through an angulated interface between two media with different refractive indices, the rays bend.

  • Mechanism of Bending: When light leaves air ($n = 1.00$) and enters glass ($n = 1.50$) at an angle, one edge of the beam enters the glass before the other. The portion remaining in the air travels at $300,000\,km/sec$, while the portion in the glass travels at $200,000\,km/sec$. This velocity difference causes the wave front to angulate. Because light travel is always perpendicular to the wave front, the beam bends.

  • Factors Governing Degree of Refraction:

    1. The ratio of the refractive indices of the two media.

    2. The degree of angulation between the interface and the entering wave front.

Application of Refractive Principles to Lenses

• Convex Lens (Convergence):

  • Parallel light rays entering a convex lens are bent toward the center.

  • Rays passing through the center strike the surface perpendicularly and do not refract.

  • Rays at the edges strike progressively more angulated interfaces and bend more toward the center.

  • Bending occurs in two stages: half when rays enter the lens, and half when they exit the opposite side.

  • Focal Point: If the lens has the proper curvature, all parallel rays will pass through a single point called the focal point.

• Concave Lens (Divergence):

  • Light rays entering the edge of a concave lens enter the lens ahead of the rays in the center.

  • This causes peripheral rays to diverge away from the central ray.

• Cylindrical Lenses vs. Spherical Lenses:

  • Spherical Lenses: Refract light at all edges (both horizontal and vertical planes) toward a central ray, focusing to a focal point.

  • Cylindrical Lenses: Bend light rays from two sides only (in one plane); the perpendicular plane remains unbent. This focuses light into a focal line.

  • Demonstration: A magnifying glass demonstrates a spherical lens (focal point); a test tube full of water demonstrates a cylindrical lens (focal line).

  • Concave Cylindrical Lenses: Diverge light rays in only one plane.

• Combination of Cylindrical Lenses: Two convex cylindrical lenses crossed at right angles perform the same function as one spherical lens of equivalent refractive power, converging all rays to a single focal point.

Focal Length and Image Formation

• Focal Length ($f$): The distance beyond a convex lens at which parallel rays converge to a common focal point.

• Effect of Source Distance:

  • If the light source is a point source nearby rather than a distant source, the entering rays are already diverging.

  • Diverging rays focus at a distance farther from the lens than the focal length of the lens for parallel rays.

  • Relationship Formula:         $\frac{1}{f} = \frac{1}{a} + \frac{1}{b}$

  • In this formula, $f$ is the focal length for parallel rays, $a$ is the distance of the point source, and $b$ is the distance of focus on the opposite side.

• Image Formation:

  • Objects are mosaics of point sources varying in brightness and color.

  • Each point source focuses on the opposite side of the lens in line with the lens center.

  • The resulting image is inverted (upside down) and reversed laterally.

Measurement of Refractive Power: The Diopter

• Refractive Power: The ability of a lens to bend light rays.

• Calculation: The refractive power in diopters is equal to $1\,meter$ divided by the focal length ($f$).

  • A lens focusing parallel rays at $1\,meter$ has a power of $+1$ diopter.

  • A lens focusing rays twice as much ($0.5\,meters$) has a power of $+2$ diopters.

  • A lens focusing at $10\,cm$ ($0.10\,meters$) has a power of $+10$ diopters.

• Concave Lenses: Power is stated as negative diopters. A concave lens that diverges light at the same rate a $1$-diopter convex lens converges light is $-1$ diopter.

• Neutralization: Placing a $-1$ diopter concave lens in front of a $+1$ diopter convex lens results in zero refractive power.

• Cylindrical Lens Strength: Computed the same as spherical lenses but must include a specified axis.

  • If the focal line is horizontal, the axis is $0$ degrees.

  • If the focal line is vertical, the axis is $90$ degrees.

Optics of the Eye

• The Eye as a Camera: The eye contains a lens system, a variable aperture (pupil), and a retina (film).

• Refractive Interfaces of the Eye:

  1. Interface between air and the anterior cornea.

  2. Interface between the posterior cornea and aqueous humor.

  3. Interface between aqueous humor and the anterior surface of the crystalline lens.

  4. Interface between the posterior surface of the lens and the vitreous humor.

• Refractive Indices ($n$) of Ocular Media:

  • Air: $1.00$

  • Cornea: $1.38$

  • Aqueous humor: $1.33$

  • Crystalline lens (average): $1.40$

  • Vitreous humor: $1.34$

• The ‐Reduced Eye": A schematic simplification where all refractive surfaces are treated as a single lens.

  • The central point of this single lens is $17\,mm$ in front of the retina.

  • Total refractive power: $59$ diopters (when accommodated for distant vision).

• Corneal vs. Lens Power:

  • Two-thirds ($39$ diopters) of the eye's power is provided by the anterior cornea because its refractive index is significantly different from air.

  • The internal lens provides only about $20$ diopters (one-third) because it is surrounded by fluids with similar refractive indices. However, the lens is critical because its curvature is adjustable for accommodation.

• Retinal Image: Inverted and reversed. The brain perceives it as upright because it is trained to consider the inverted image as normal.

Mechanism of Accommodation

• Definition: The process of increasing the refractive power of the lens to focus on near objects.

• Range in Children: Refractive power can increase from $20$ diopters to approximately $34$ diopters (an accommodation of $14$ diopters).

• Physical Mechanism:

  • In youth, the lens is a strong elastic capsule filled with viscous, proteinaceous fluid.

  • Relaxed State: If no tension exists on the capsule, the lens assumes an almost spherical shape due to its own elasticity.

  • Suspensory Ligaments (Zonules): About $70$ ligaments attach radially around the lens, pulling the edges toward the outer eyeball. These ligaments are normally tensed, keeping the lens relatively flat for distant vision.

  • Ciliary Muscle: Located at the attachment of the ligaments. It has two sets of smooth muscle fibers:

    1. Meridional Fibers: Extend from peripheral suspensory ligaments to the corneoscleral junction. Contraction pulls the insertions medially toward the cornea, releasing ligament tension.

    2. Circular Fibers: Arrange circularly around ligament attachments. Contraction creates a sphincter-like action, decreasing the circle's diameter and relaxing ligament tension.

  • The Result: Contraction of either ciliary fiber set relaxes the ligaments, allowing the lens to become thicker/more spherical, increasing its dioptric power.

• Nerve Control: Accommodation is controlled by parasympathetic nerves transmitted via the third cranial nerve from the third nerve nucleus in the brain stem. Sympathetic stimulation has a very weak effect in relaxing the ciliary muscle.

• Presbyopia (Loss of Accommodation):

  • As age increases, the lens grows larger, thicker, and less elastic (partly due to protein denaturation).

  • Decline: Accommodative power drops from $14$ diopters in children to less than $2$ diopters at age $45\text{--}50$ and essentially $0$ diopters by age $70$.

  • Correction: Bifocal glasses (upper segment for far vision, lower for near vision).

Pupillary Diameter and Depth of Focus

• Major Function of the Iris: Regulates light entry. The amount of light is proportional to the square of the pupillary diameter.

• Pupil Range: Approximately $1.5\,mm$ to $8\,mm$ in diameter, allowing a $30$-fold change in light entry.

• Depth of Focus:

  • Increases with decreasing pupillary diameter.

  • A small aperture ensures that even if the retina is displaced from the focal plane, the light rays do not diverge much, preventing "blur circles."

  • Greatest depth of focus occurs when the pupil is extremely small, as central rays are always in focus.

Errors of Refraction

• Emmetropia (Normal Vision): Parallel light rays from distant objects focus sharply on the retina when the ciliary muscle is relaxed.

• Hyperopia (Farsightedness):

  • Cause: Eyeball is too short or lens system is too weak.

  • Effect: Parallel rays focus behind the retina.

  • Correction: Use of accommodation to focus distant objects (if muscle power is sufficient). In old age (presbyopia), accommodation fails. Correction requires a convex lens ($+$).

• Myopia (Nearsightedness):

  • Cause: Eyeball is too long or lens system has too much power.

  • Effect: Parallel rays focus in front of the retina. No natural mechanism can decrease lens power to correct this.

  • Limit: There is a specific "far point" for clear vision. Correction requires a concave lens (-$).\n* **Astigmatism:**\n * **Cause:** Uneven curvature of the cornea (e.g., shaped like an egg lying sideways) in one plane compared to the other.\n * **Effect:** Light in the vertical plane (BD) might be refracted more than in the horizontal plane (AC), resulting in no common focal point. \n * **Accommodation:** Cannot compensate because it changes curvature equally in both planes.\n * **Correction:** A spherical lens to correct one plane, plus a cylindrical lens at a specific axis and strength to correct the other plane.\n * **Determination of Axis:** Use of parallel black bars (astigmatism chart). The axis of the fuzzy bars indicates the axis of the out-of-focus cylindrical component.\n* **Contact Lenses:**\n * Held by tear fluid; the tears' refractive index (1.38) matches the cornea, nullifying corneal refraction.\n * The outer surface of the contact lens substitutes for the cornea.\n * **Advantages:** Corrects keratoconus (bulging cornea), allows a broader field of view, and minimizes image size distortion compared to traditional glasses.\n\n# Visual Acuity and Cataracts\n\n* **Cataracts:** Cloudy or opaque areas in the lens caused by protein denaturation and coagulation. Corrected by surgical removal and implantation of an artificial plastic lens.\n* **Retinal Resolution:**\n * The theoretical point source forms a spot approximately 11\,\mu m in diameter on the retina.\n * Foveal cones have a diameter of 1.5\,\mu m.\n * Two separate points can be distinguished if their centers are at least 2\,\mu m apart on the retina.\n * **Angular Resolution:** Normal acuity is about 25$seconds of arc. At$10\,meters$, two points can be distinguished if they are$1.5$to$2\,mm apart.\n* **Foveal Area:** Maximum acuity is limited to the fovea (diameter <0.5\,mm$), covering less than$2$degrees of the visual field. Acuity decreases$10-fold toward the periphery as more receptors connect to single optic nerve fibers.\n* **Clinical Testing:** Snellen chart at 20\,feet.\n * 20/20: Normal vision.\n * 20/200$: Can see at$20\,feet$what a normal person sees at$200\,feet.\n\n# Depth Perception and Ophthalmoscopy\n\n* **Depth Perception Mechanisms:**\n 1. **Sizes of Retinal Images:** The brain knows the actual size of common objects (e.g., a 6-foot-tall person) and calculates distance automatically.\n 2. **Moving Parallax:** Moving the head causes near objects to move across the retina faster than distant objects.\n 3. **Stereopsis (Binocular Vision):** Eyes are >2\,inches$apart. For near objects, images on the two retinas are in different positions. This is useless for distances beyond$50$to$200\,feet.\n* **Ophthalmoscope:**\n * Allows an observer to see another retina. \n * If both eyes are emmetropic and looking at each other, the light from the observed retina focuses on the observer’s retina.\n * Correction Turret: Ophthalmoscopes have a series of lenses. Since a normal young adult's eye accommodates by about +2$diopters during the exam, a setting of approximately$-4 diopters is often required to achieve focus.\n\n# Fluid System of the Eye\n\n* **Intraocular Fluid:** Maintains pressure to keep the eyeball distended.\n * **Aqueous Humor:** Freely flowing fluid in front of the lens.\n * **Vitreous Humor (Vitreous Body):** Gelatinous mass behind the lens. Contains a fine fibrillar network of proteoglycan molecules. Allows slow diffusion but little flow.\n* **Formation of Aqueous Humor:**\n * Formed at 2\,to\,3\,\mu l/min by the ciliary processes (folds on the ciliary body).\n * Surface area: 6\,cm^2 in each eye.\n * **Mechanism:** Active transport of sodium (Na^+$) into epithelial spaces pulls chloride ($Cl^-$) and bicarbonate ($HCO_3^-) to maintain neutrality. This creates osmotic pressure that pulls water into the anterior chamber. Also involves active transport of glucose and amino acids.\n* **Outflow Pathway:**\n * Flows through the pupil into the anterior chamber.\n * Passes into the angle between the cornea and iris (iridocorneal angle).\n * Percolates through the trabecular meshwork (openings of 2\,to\,3\,\mu m).\n * Enters the Canal of Schlemm (a thin-walled vein circling the eye).\n * Small "aqueous veins" lead into extraocular veins.\n* **Intraocular Pressure (IOP):**\n * Average: 15\,mm\,Hg$(Range:$12\,to\,20\,mm\,Hg).\n * Measurement: Tonometry. A plunger displaces the anesthetized cornea; the amount of displacement equates to pressure.\n * **Glaucoma:** Pathological increase in IOP, sometimes up to 60\,to\,70\,mm\,Hg.\n * **Damage Mechanism:** Pressures >25\,to\,30\,mm\,Hg$$ over time compress the optic nerve at the optic disc, blocking axonal flow of cytoplasm and reducing nutrition.

  • Causes: Increased resistance in trabecular spaces (white blood cells/debris in inflammation or fibrous occlusion in aging).

  • Treatment: Drugs to reduce secretion/increase absorption, or surgery to open trabeculae or create subconjunctival drainage channels.