If we study the behavior of these rays at refracting and reflecting surfaces, we can learn to determine how images are formed by optical systems, where they are located, and how large they are.

Point Sources, Pencils, and Beams of Light

You can think of a distant star as a point source of light, as its apparent size is so small. If we cut off a portion of the bundle of rays of light that emanate from a point source by placing an aperture in their path, the light that passes through the hole is called a pencil of rays (Fig 1-4). The rays passing just inside the edges of the aperture are called limiting rays. The rays of a pencil of light are divergent, parallel, or convergent in the direction of travel of the light (Fig 1-5). Waves of light naturally diverge from their source but can become convergent if they are redirected, for instance, by passing through a convex lens.

Figure 1-4 Point source of light and an aperture, creating a pencil of rays. (Redrawn from Basic and Clinical Science Course

Section 2: Optics, Refraction, and Contact Lenses. San Francisco: American Academy of Ophthalmology; 1986–1987:38. Fig 1.)

Figure 1-5 Divergent, parallel, and convergent pencils of light. (Redrawn from Basic and Clinical Science Course Section 2: Optics,

Refraction, and Contact Lenses. San Francisco: American Academy of Ophthalmology; 1986–1987:39. Fig 2.)

A beam of light includes many bundles of light that arise from the points of an extended source (Fig 1-6). A light bulb and the sun are examples of extended sources of light, and the objects you see around you are extended sources of reflected light. A slide projector emits a mildly diverging beam of convergent pencils of light, each of which has been focused by a lens to converge to points on the screen across the room, forming a larger picture on the screen of the smaller picture on the slide. (See Clinical Example 1-1.)

Figure 1-6 A beam of light, consisting of pencils emanating from many point sources, that is being limited by an aperture.

(Redrawn from Basic and Clinical Science Course Section 2: Optics, Refraction, and Contact Lenses. San Francisco: American Academy of Ophthalmology; 1986–1987:39. Fig 3.)

Clinical Example 1-1

The concept of conjugate points is illustrated by retinoscopy. When performing retinoscopy, the examiner observes light emanating from the patient’s retina and passing through the patient’s pupil. Because the examiner is observing the light at the patient’s pupil, the examiner’s retina is conjugate with the patient’s pupil (Fig 1-7A). At the point of neutrality in the refraction, the patient’s retina is conjugate with the peephole of the retinoscope (Fig 1- 7B). Adjustment for the distance between the examiner and the patient (working distance) makes the patient’s retina conjugate with optical infinity (Fig 1-7C). (Retinoscopy is covered in detail in Chapter 3, Clinical Refraction.)