2.1 Lens Characteristics & Powers

Understanding Optical Materials and Refraction

When light travels from one medium to another, such as from air into an ophthalmic lens, its velocity changes. This change in speed causes the light to bend, a physical phenomenon known as refraction. The degree of bending depends on the optical density of the lens material compared to the surrounding air. To quantify this property, we use the index of refraction (denoted as n), which is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in the specific medium (v):

n = c / v

Because light travels slower in any material than in a vacuum, the index of refraction is always greater than 1.00. Standard ophthalmic crown glass has a refractive index of 1.523, whereas modern plastic materials range from 1.498 (CR-39) to 1.74 (ultra-high-index plastics). A material with a higher refractive index bends light more efficiently. Practically, this means that for any given prescription, a higher-index lens requires less surface curvature (flatter curves) to achieve the same optical power. Flatter curves translate directly into thinner profile lenses.

However, choosing a lens material is a balance of three primary physical characteristics:

1. Refractive Index: Determines the thickness of the lens.
2. Abbe Value: Determines the optical clarity and dispersion.
3. Density (Specific Gravity): Determines the physical weight of the lens.

While higher-index materials allow for thinner lenses, they also tend to have a higher density and a lower Abbe value. Therefore, a high-index lens is not always the best choice for every patient, particularly those with low prescriptions who would benefit more from the lightweight properties and superior optical clarity of materials like Trivex or CR-39.

Thick Lens Power vs. Thin Lens Power

In basic optical training, lenses are often treated as infinitely thin, meaning their thickness is neglected. Under the thin lens approximation, the power of a lens is simply the sum of its front and back surface powers. However, real ophthalmic lenses have a physical thickness (t) that affects how light propagates through them. This distinction becomes critical in high-power prescriptions (typically above +/-4.00 diopters).

To account for thickness, we define thick lens power using vertex powers. There are two primary vertex powers:

• Back Vertex Power (BVP): The optical power measured from the back surface of the lens to its focal point. BVP is the industry standard for ophthalmic prescriptions. When an optometrist or ophthalmologist writes a prescription, they are specifying BVP. Standard lensmeters (manual or automated) are designed to measure BVP when the temple side of the frame is held against the lens stop.
• Front Vertex Power (FVP): The optical power measured from the front surface of the lens to its focal point. FVP is primarily used when neutralizing the add power of multifocal lenses (such as flat-top bifocals), as the segment is placed on the front surface of the lens.

In high-minus lenses, the center is thin, so the difference between BVP and nominal power is negligible. However, in high-plus lenses, the center thickness is substantial, and neglecting the thickness would lead to significant errors in the final prescription. The shape of the lens (its thickness and front curve) creates a "shape factor" that adds positive power to the lens, which must be compensated for during laboratory manufacturing.

Lens Thickness, Base Curve, and Diameter

The final thickness of an ophthalmic lens is determined by a complex interaction between the lens power, the base curve (the standardized front surface curve of the lens blank), the index of refraction of the material, and the lens diameter (often referred to as the aperture or blank size).

For any lens, the curvature of the front and back surfaces dictates the optical power. To create a plus lens (which converges light), the center must be thicker than the edges. Conversely, to create a minus lens (which diverges light), the edges must be thicker than the center.

The mathematical tool used to describe this curvature and calculate thickness is the sagitta (often abbreviated as "sag" and denoted as s). The sagitta is the perpendicular distance from the center of a curve to a chord representing the lens diameter. The relationship between sagitta, lens radius of curvature (r), and half-diameter (y) is governed by the sag formula.

Importantly, the thickness of a lens scales exponentially with its diameter. For a plus lens, if you increase the frame size (and thus the lens diameter), the center thickness must increase significantly to maintain the required edge thickness (which must be a minimum of 1.0mm to 2.0mm for safety and mounting). For a minus lens, a larger frame size results in much thicker outer edges. Therefore, minimizing the lens diameter through proper frame selection is the most effective way to reduce lens thickness and weight, regardless of the material chosen.

Dispersion, Abbe Value, and Chromatic Aberration

Light is composed of a spectrum of colors, each traveling at a slightly different wavelength. Short wavelengths (blue/violet light) bend more than long wavelengths (red light) when passing through a lens. This separation of white light into its component colors is called dispersion.

In ophthalmic optics, we measure a material's dispersion using the Abbe value (also known as the V-number or constringence). The Abbe value is named after the physicist Ernst Abbe and is defined as:

V = (n_d - 1) / (n_F - n_C)

Where n_d, n_F, and n_C are the refractive indices of the material at specific spectral lines of helium, hydrogen, and sodium, respectively. Crucially, the Abbe value is inversely related to dispersion:

• High Abbe Value (e.g., 58): Low dispersion, meaning light is split very little, resulting in superior peripheral optical clarity.
• Low Abbe Value (e.g., 30): High dispersion, meaning light is split significantly, leading to unwanted optical distortions.

When dispersion occurs in an ophthalmic lens, it produces chromatic aberration. Chromatic aberration manifests as colored fringes (typically blue/orange or red/green halos) around high-contrast objects, especially when the patient looks through the periphery of the lens. The amount of lateral chromatic aberration (CA) in prism diopters can be calculated using the formula:

CA = D / V

Where D is the dioptric power of the lens and V is the Abbe value.

For example, a +6.00 D polycarbonate lens (V = 30) will induce 6.00 / 30 = 0.20 diopters of chromatic aberration at the edge. A patient will likely notice this color fringing. If the same prescription is made in Trivex (V = 44), the chromatic aberration is reduced to 6.00 / 44 = 0.14 diopters, which is below the human threshold of detection for most individuals. Patients who are highly sensitive to chromatic aberration often complain of peripheral blur, headaches, or "rainbows" when switched from CR-39 or Glass to Polycarbonate.

Comparison of Ophthalmic Lens Materials

To assist in material selection, the table below outlines the critical characteristics of the most common lens materials used in modern opticianry.