Geometrical Optics and Vision Correction: Understanding Light and Eyesight
Geometrical Optics: Principles and Applications
Geometrical optics deals with the phenomena of light rays, including reflection, refraction, and analysis of their deviations. It is based on these assumptions: light travels in a straight line in a homogeneous and isotropic medium, and the reflection and refraction of light rays are reversible and comply with Snell’s law.
Diopters and Optical Systems
A diopter is the surface of an optical system separating two different environments with varying refractive indices. It can be spherical or flat.
Single Optical Systems
- Spherical Diopter: Separates two transparent environments with different refractive indices. It has a radius of curvature (R). Convex (R>0) or concave (R<0).
- Flat Diopter: A flat surface separating two transparent environments with different refractive indices.
- Mirror: A smooth surface that reflects light rays. It can be flat or spherical (concave or convex). The radius of curvature (R) of a mirror can be positive or negative, depending on whether it’s concave or convex, and whether the reflective surface is internal or external.
Compound Optical Systems
- Centered Optical System: A series of diopters whose centers lie on a straight line called the optical axis.
- Lenses: A centered optical system consisting of two diopters, where at least one is spherical. Both environments have refractive indices. Lenses are used to correct vision and in cameras.
Lenses can be:
- Convergent: Thicker in the center. Types include biconvex (R1>0, R2<0), plano-convex (R1 = ∞, R2<0), and meniscus (R1>0, R2>0 and R1<R2).
- Divergent: Thicker at the edges. Types include biconcave (R1<0, R2>0), plano-concave (R1 = ∞, R2>0), and meniscus concave (R1<0, R2<0 and |R1| < |R2|).
Vision Correction: Common Eye Conditions
Let’s examine the most common vision errors, considering the eye as a centered optical system. These can be corrected with glasses or contact lenses.
Myopia (Nearsightedness)
People with myopia can focus on nearby objects but not distant ones. The remote point is at a finite distance. Myopic eyes cannot see objects clearly beyond this distance.
The eye’s refractive surfaces are too convergent, or the eyeball is too long. Images form *before* the retina.
Correction: Divergent lenses are used. These lenses cause light rays to diverge, allowing the crystalline lens to focus them on the retina.
Hyperopia (Farsightedness)
Hyperopia causes difficulty focusing on nearby objects. The near point is farther than the standard 25 cm.
The crystalline lens isn’t convergent enough, or the eyeball is too short. Images form *behind* the retina, causing blurred vision.
Correction: Convergent lenses are used. These lenses cause light rays to converge, allowing the crystalline lens to focus them on the retina.
Astigmatism
In astigmatism, the eye’s refractive surfaces, especially the cornea, are not perfectly spherical. Instead of a single focal point, two linear images are formed. People with astigmatism cannot focus on both vertical and horizontal lines simultaneously.
Correction: Lenses with different radii of curvature in perpendicular directions are used.
Presbyopia (Age-Related Farsightedness)
Presbyopia is the gradual loss of near vision, often called “tired vision.” It’s typically caused by the crystalline lens losing flexibility with age, reducing the eye’s ability to accommodate and focus on near objects. Images do not form clearly.
Correction: Convergent lenses are used.
Typical Near Point Progression with Age:
- Age (years): 10, 20, 30, 40, 50, 60
- Near point (cm): 7, 10, 14, 22, 40, 200