Wavelength of light. Electromagnetic radiation exists in many forms. The characteristic of the radiation that determines the form in which it is encountered is the wavelength. Long wavelengths are encountered as radio transmissions or radar; these emit a low energy. Short wavelengths are encountered as cosmic rays and x-rays; these emit a high energy. The visible portion of the electromagnetic radiation spectrum occurs between the ultraviolet and infrared portions, from 380 nm at the violet end of the spectrum to 760 nm at the red end.

Frequency of light waves. The frequency of electromagnetic radiation is the number of times a particular position on the wave passes a fixed point in a fixed interval of time. It is inversely related to the wavelength. For example, radio waves, which occur as long wavelength radiation, have a frequency of 10⁴ cycles to 10⁸ cycles per second (cps), whereas the visible part of the spectrum is in the 10¹⁴ cps to 10¹⁵ cps range and includes shorter wavelength radiation.

Velocity of light waves. The entire spectrum of electromagnetic waves travels at a speed of 3 × 10⁸ m per second (186,000 miles per second) in a vacuum. The wavelength and frequency of light can be spoken of interchangeably because they are related through the following equation: wavelength × frequency = velocity of light = 3 × 10⁸ m per second.

Index of refraction. Although the frequency of light does not vary with the density of the medium through which it is traveling, the speed is reduced in a dense medium. The ratio of the velocity of light in a vacuum to the velocity of light in a particular medium (n/n′) is referred to as the index of refraction for that medium. Because the frequency of radiation does not vary with the medium and the speed does, it follows that the wavelength in a dense medium is less than it is in air and is proportional to the change in speed. Each medium, therefore, has a different refractive index for a given wavelength. Short wavelengths, or blue light, are slowed down or refracted more than long wavelengths, or red light. This accounts for the chromatic aberration present in the eye or in single-element lens systems. The visible spectrum is defined in relationship to chromatic aberration and is described by the use of the C (red) – F (blue) line.

Quanta or photons. The energy in electromagnetic radiation is measured in units called quanta or photons. The energy of an individual photon is proportional to the frequency or inversely proportional to the wavelength. Therefore, the energy of a photon at 400 nm is twice as great as that of a photon at 800 nm. For example, red light is innocuous, ultraviolet light produces burns, and x-rays produce severe damage to tissues.

Loss of light by reflection or absorption. With respect to the eye, the light incident on the retina from a light source is decreased by loss from reflection or absorption at the cornea, lens, and retinal surfaces. Although the cornea is quite transparent from 400 to 1,200 nm, the crystalline lens does absorb some of the radiant energy, particularly short wavelengths. The young, healthy lens transmits incident light of 320 nm. Absorption at the blue end of the visible spectrum increases with age as xanthochromic (yellow-brown) proteins accumulate in the lens.
Some of the short wavelength radiation is also absorbed by the yellow pigment in the macular region of the retina.

Color of light. The physical stimulus that is responsible for the sensation of color is the wavelength of the radiation. Wavelength in the region around 430 nm produces a violet hue, around 460 nm blue, around 520 nm green, around 575 nm yellow, around 600 nm orange, and around 650 nm red. A mixture of wavelengths, such as that which occurs in sunlight, produces a white hue. It is also worth noting that objects appear as a particular color because they preferentially reflect wavelengths of that color and absorb the other wavelengths.

Reflection. When light rays strike a smooth surface, they may bounce off the surface, or be reflected, rather than pass through. Reflection from a polished surface is referred to as “regular” or “specular” reflection. This does not occur randomly but follows a simple rule—the angle of reflection is equal to the angle of incidence and lies in the same plane. The angle of reflection and the angle of incidence are measured relative to the surface perpendicular at the point of impact. When light is reflected, a plane or flat mirror reverses the direction of the light rays only and does not effect vergence, so no magnification, minification, or image inversion occurs. Convex or concave reflective surfaces can change the vergence of light rays and focus them, resulting in an altered image. This has a practical significance for spectacle wearers. Reflections from the ocular surfaces of corrective lenses can produce virtual images near the far point plane of the eye, images that can be annoying to the patient. The images can be eliminated by tilting the lenses or using an antireflective coating. The cornea can also be used as a reflective surface. The principal of keratometry depends on the anterior surface of the cornea, which acts as a concave mirror. By measuring the size of the reflected image, the cornea’s radius of curvature can be calculated. The cornea is also employed as a reflecting surface when checking it for irregularity with a keratoscope. By examining the reflected images of a series of concentric circles, one can check for distortion.

Refraction of light. When rays of light traveling through air enter a denser transparent medium, the speed of the light is reduced and the light rays proceed at a different angle (i.e., they are refracted). The one exception is when the rays are incident perpendicular to the surface (collimated or paraxial light). In this case the speed of the light is reduced, but the direction of the light is unchanged.

Spherical lenses have equal radii of curvature in all meridians.

Toric lenses are shaped like a section through a football. One meridian is more curved than all of the others, and the meridian perpendicular to the steepest meridian is flatter than all of the other meridians. In a toric lens, the meridians of least curvature and the greatest curvature are always at right angles to one another and are referred to as the principal meridians. Toric lenses are prescribed to correct astigmatism. Toric lenses can be identified by observing a vertical contour such as a window or door frame through the center of the lens and rotating the lens in a vertical plane (parallel to the surface that is being observed). If the lens is a toric lens, the edge of the vertical contour is broken or discontinuous in the area viewed through the lens. The image will also appear to rotate clockwise or counterclockwise as the lens is rotated back and forth. If the same vertical contour is viewed through the center of a spherical lens, it remains continuous when viewed within and outside the borders of the lens and does not appear to rotate when the lens is rotated. Toric lenses can be plus lenses, minus lenses, one principal meridian plus and the other minus, meniscus lenses, or they can be fabricated in a planocylinder form in which one principal meridian has zero optical power. Toric lenses are also referred to as spherocylinders.

Prisms. A prism is an optical device composed of two refracting surfaces that are inclined toward one another so they are not parallel. The line at which the two surfaces intersect is the apex of the prism. The greater the angle formed at the apex, the stronger the prismatic effect (Fig. 14.3A[1]). Because the two surfaces of a prism are usually flat, they alter the direction of the light rays, but not their vergence. An object viewed through a prism appears to be displaced in the direction of the prism apex, but the focus is not altered and no magnification or minification occurs. Prisms are usually prescribed to assist a patient with an extraocular muscle imbalance, which results in a deviation of one visual axis relative to the other, so that the patient may achieve single binocular vision or do so more comfortably. They may be oriented in the spectacle correction so as to produce horizontal, vertical, or both horizontal and vertical displacement, as needed. The strength of a prism is measured in prism diopters (pds). The prism power is equal to the displacement in centimeters of a light ray passing through the prism measured 1 m from the prism. (Each diopter displaces a ray of light 1 cm at a distance of
1 m.) Two prism diopters of displacement are approximately equal to 1 degree of arc.

Lensometers are precision instruments used to measure the spherical power, cylindrical (toric) power and the corresponding axis, and prism power, if present, of a spectacle or contact lens. Synonyms include: vertometer, vertexometer, dioptometer, and focimeter.

Retinoscopy is an objective method of analyzing the optics of the patient’s eye to determine the refractive error. A retinoscope is a handheld instrument that the examiner uses to illuminate the inside of the patient’s eye and observe the light rays (reflected from the retinal pigmented epithelium and choroid) as they emerge from the patient’s eye. This process involves moving the streak of light back and forth across a series of lenses held in front of the patient’s pupil, resulting in a linear light reflex moving in the same (hyperopia) or opposite direction (myopia) as the light. The filling of the entire pupil with light that does not move indicates neutralization of the refractive error in that meridian and is the end-point reading for that meridian. The linear streak of light can be rotated 360 degrees through the pupil to examine different meridians of the eye. In the case of astigmatism, the retinoscope linear light must be empirically lined up along a principal meridian (the clearest light streak as the retinoscope light is rotated) and plus or minus lenses put up until movement of light in that meridian is neutralized and the lens power recorded. This is repeated in the meridian 90 degrees away for the second lens and axis. By knowing what lenses are required, it is a simple matter to calculate the amount of ametropia. Opacities of the media, tiny pupils, poor fixation by the patient, or distortion of the light reflex can all be troublesome. Prescribing lenses on the basis of retinoscopic findings alone can too often result in a prescription that is not well tolerated by the patient.

Subjective refraction is a tool whereby the examiner relies on patient responses to narrow the prescription further. Retinoscopy or automated refraction findings or habitual spectacle power may be the starting guide for subjective refraction. In the absence of astigmatism, the refraction is simply a matter of adding more plus or minus power until the patient reads his or her best visual acuity with the most plus or least minus power. In the presence of astigmatism, and to help test for it, the fogging technique is very effective (see Section VI.B.3.e). Refractions involving astigmatism are best refined by the Jackson cross-cylinder (JCC) technique (see Section VI.B.3.f), which may be done manually or by an automated refractor.

Automated refraction. In recent years, electronic microcircuitry and computer technology have combined to develop sophisticated instruments for refracting patients. In general, automated refractometers are highly accurate. The instrument must be properly in line with the patient’s visual axis, accommodation must be relaxed, the pupil must be of satisfactory size, and the media must be sufficiently clear. The primary role for these instruments is increased efficiency with which eye
care is delivered by obtaining the approximate refractive error, which then should be manually refined by the refractionist. For example, an automated refractor may indicate a cylinder axis of 15 degrees, but the patient’s habitual spectacles are at axis 10 degrees without discomfort. Often, it is wiser to give the axis 10 degrees with perhaps some sacrifice of visual clarity than axis 15 degrees, which is clear but feels “uncomfortable.”

Cycloplegic refraction. Cycloplegia is the employment of pharmaceutical agents to temporarily paralyze the ciliary muscle, thus stabilizing the eye’s accommodative reflex and allowing for the measurement of a definitive end point. Cycloplegic refraction is particularly useful in young patients with highly active accommodation. This ensures complete relaxation of the ciliary muscle, allowing for the accurate measurement of the ametropia in young hyperopes, thereby avoiding overcorrection. Methods of inducing cycloplegia include 1% cyclopentolate or tropicamide, one drop q5min for two applications in the office 20 minutes prior to refraction, or atropine 1%, one drop tid for 3 days before the refraction.

Chromatic aberration. The index of refraction for any transparent medium varies with the wavelength of the incident light. This variation is such that blue light is refracted more than red light (Fig. 14.3A[2]). This accounts for the chromatic dispersion that occurs when white light is passed through a prism and a rainbow effect is produced. In a convex or plus lens, blue light is focused slightly closer to the lens than red light. The same is true of the human eye, in which blue light is focused slightly in front of red light.

Spherical aberration. In most discussions of optics, certain assumptions are made for the sake of simplicity. Higher-order optics become quite complex and contribute little to the understanding of basic measuring and prescribing of spectacles. So far, it has been assumed that all light rays from an object that pass through a lens come to focus at a single image point. A closer analysis reveals that this is true only for light rays that are paraxial (i.e., that pass through the center of the lens). Those light rays that are parallel to the axis but that pass through the periphery of the lens are usually refracted more than the paraxial rays. Peripheral rays will focus closer to the lens (Fig. 14.3B). Every object point on the axis of the lens will then be represented by a blur circle rather than a point focus. The size of this blur circle can be reduced by restricting the passage of light through the lens to the central portion, as is done when an object is viewed through a pinhole aperture. This same effect accounts for the increased depth of focus obtained when the iris diaphragm of a camera is reduced in size or when the pupil of the eye is constricted. Spherical aberration may produce a variable concentric retinoscopic reflex in patients with large pupils, with the peripheral portions of the pupil appearing myopic (against motion) while the central portion is at neutrality.

Radial astigmatism occurs when light rays pass through a lens obliquely. Instead of focusing a point of light as a point image, two linear images form at right angles to one another with a “circle of least confusion” between them. This form of aberration is of no great significance in the eye; however, it can create considerable blurring of the image formed by spectacle lenses.

Distortion is the result of differential magnification in an optical system. This occurs because light from some parts of the object is focused by the central portion of the lens, while other parts are focused by peripheral portions of the lens. In other words, the shape of the image formed does not correspond exactly to the shape of the object. For practical purposes, this is not a problem in the eye, but it can be troublesome in higher-powered spectacle lenses. High plus lenses produce “pincushion” distortion, and high minus lenses result in “barrel” distortion.

The cornea contributes approximately two-thirds of the refracting power of the eye. This is true because more deflection of light rays occurs at the air-cornea interface because of the large difference in index of refraction between these two media. The crystalline lens is in fact a more powerful refracting lens than the cornea in air because it is biconvex and each of its surfaces is more convex than the cornea. The lens, however, is in the aqueous–vitreous medium, and the difference in refractive index at the aqueous–lens and lens–vitreous interfaces is much less. The cornea has an index of refraction of 1.376 and contributes +43 D to the eye.

The crystalline lens has an index of refraction that increases from the cortex to the nucleus, but averages 1.41 with a power of +20 D. Because these two refracting elements are separated, the total power of the eye is not their sum but the equivalent power of +58.7 D.

The pupil is also a significant component of the eye’s optical system. It can constrict, reducing the amount of light that enters the eye, decreasing aberrations, and increasing the eye’s depth of focus. This accounts for the ability of many people who require glasses to get along without them when the illumination is good.

The retina is a unique kind of film. It contains the “coarse grain” but highly sensitive rods for registering images at very low levels of illumination and the “fine grain” color-sensitive cones for high resolution and discrimination at high levels of illumination. Only one or two quanta of light energy are required to activate the rods. On the other hand, rapid neural adaptation and the more gradual process of adjusting the steady state between bleaching and regeneration of retinal visual pigments enable the retina to function perfectly at extremely high levels of illumination. What other film functions so well both in moonlight and at high noon? The manner in which visual images are formed, transmitted to the visual cortex, and interpreted is a fascinating story but not appropriate to this discussion.

Emmetropia. The eye is considered to be emmetropic if parallel light rays from an object more than 6 m away are focused at the plane of the retina when the eye is in a completely relaxed state. An emmetropic eye will have a clear image of a distant object without any internal adjustment of its optics. Although most emmetropic rays are approximately 24 mm in length, a larger eye can be emmetropic if its optical components are weaker, and a smaller eye can be emmetropic if its optical components are stronger.