Optics Lessons: Part 8 - Optical Instruments

The Human Eye

The human eye is the most fundamental optical instrument, since without it the field of optics would not exist. Before we take a look at the human eye, here are some words you should be familiar with before reading this section.

Crystalline lens, Retina, Rods, Cones, Accommodation, Nearsightedness, Farsightedness, Astigmatism, Circle of Least Confusion, Far Point, Near Point

The eye has a converging lens that focuses images on the light-sensitive lining on the rear surface inside the eyeball. The iris is a circular diaphragm that opens and closes to adjust the amount of light entering the eye. The human nervous system analyzes image signals from the eye at the rate of about 30 times per second. The eye might therefore be likened to a movie or video camera, which exposes a similar number of images per second.

The eyeball is a nearly spherical chamber with an internal diameter of about 15 cm and filled with a jellylike substance called the vitreous humor. The has a white outer covering called the sclera, part of which is visible as the white of the eye. Light enters the eye through a curved, transparent tissue called the cornea and passes into a clear fluid known as the aqueous humor. Behind the cornea is a circular diaphragm, the iris, whose central hole is called the pupil. The iris contains the pigment that determines eye color. Through muscle actions, the iris can change the area of the pupil, thereby controlling the amount of light entering the eye.

Vision Defects

The eyes of many people cannot accommodate within the normal range of 25 cm to infinity. These people have one of the two most common visual defects: nearsightedness (myopia) and farsightedness (hyperopia).

Nearsightedness arises because the eyeball is to long or because the curvature of the cornea is too great. For whatever reason, the images of distant objects are focused in front of the retina instead of focusing on the retina.

Correcting Nearsightedness

Nearsightedness can be corrected by using the appropriate diverging lens. Such a lens causes the rays to diverge, and the eye focuses the image father back so that it falls on the retina.

When the near point is not at the normal position but at some point farther from the eye, the farsightedness occurs. The image of an object that is closer to the eye than the near point is formed behind the retina. Farsightedness arises because the eyeball is too short or because of an insufficient curvature of the cornea. A similar farsighted called presbyopia occurs with the normal receding of the near point with age.

Correcting Farsightedness

Appropriate converging lenses usually correct farsightedness. Such a lens causes the rays to converge, and the eye is than able to focus the image on the retina.

When a person has astigmatism, their eyes have different focal lengths in different planes. Points may appear as lines, and the image of a line may be distinct in one direction and blurred in another or blurred in both directions in the circle of least confusion.
Astigmatism may be corrected with lenses that have greater curvature in the plane in which the cornea or crystalline lens has deficient curvature. Astigmatism is lessened in bright light because the pupil of the eye becomes smaller and the circle of least confusion is reduced.

What is meant by 20/20 vision anyway?

Visual acuity, or sharpness, is a measure of how vision is affected by object distance. This is usually measured by the chart of little letters the nurse makes you read at the doctor's office. The result is usually expressed as a fraction. The numerator is the distance at which the test eye sees a standard symbol clearly, and the denominator is the distance at which the letter is seen clearly by a "normal" eye. A 20/20 (test/ normal) rating, which is called "perfect" vision, just means that at a distance of 20 feet the eye being tested can see standard-sized letters as clearly as can a normal eye.

A person's eye may have differing visual acuity. For example, one eye may have 20/20 vision while the other 20/30. When the numerator is lower than the denominator, such as 20/30, it just means that the eye being tested can read standard-sized letters from a chart at a distance of 20 feet while someone with normal vision could do so at 30 feet. n other words, the eye being tested has to be closer to the object than a normal eye would to see the object clearly. In the reverse case, for argument's sake a 20/15 vision eye, it would indicate that the test eye could see an object clearly from a distance of 20 feet, whereas a normal eye would have to be a distnace of 15 feet to do so. Thus, the greater the ratio or fraction, the better the visual acuity of the eye.

Microscopes

Microscopes are used to magnify objects so that we can see more detail or see features that are normally not visible to the unaided eye. There are two basic types of icroscopes that we will cover in this part of the site: simple and compound microscopes. Here are a few terms you need to know:

Magnifying Glass, Angular Magnification

The Magnifying Glass (The Simple Microscope)

How large an object appears depends on the size of the image on the retina. This may be related to the angle subtended by the object; the greater the angle, the bigger the image.

A magnifying glass allows a clear image to be formed of an object that is closer than the near point. In such a position, an object subtends a greater angle and therefore appears larger, or magnified. The lens produces a virtual image beyond the near point on which the eye focuses.

The maximum angular magnification occurs when the image seen through the glass is at the eye's near point, that is di= -25 cm, since this is as close as it can be clearly seen.(For discussion sake, a value of 25 cm will be assumed to be typical for near point. The minus sign is used because the image is virtual.) The corresponding object distance may be calculated from the thin lens equation:

Thus, lenses with shorter focal lengths give greater angular magnification.

The Compound Microscope

A basic compound microscope consists of a pair of converging lenses, each of which contributes to the magnification. The converging lens with a relatively short focal length (fo< 1cm) is known as the objective.

The objective lens produces an inverted, real and enlarged image of an object positioned slightly beyond the focal point. The other lens, called the eyepiece or ocular, has a longer focal length (fe is a few centimeters) and is positioned so that the image formed by the objective falls just inside the focal point. This lens creates a magnified virtual image that is viewed by the observer. For comparison, think of the objective as a projector, and the eyepiece is a simple magnifying glass used to view the projected image.

The total magnification (m total) of a lens combination is the product of the magnifications produced by the two lenses. In other words, in order to find the magnification power of the microscope, just multiply the eyepiece magnification with the objective magnification. The image formed by the objective is larger than its object by a factor Mo equal to the lateral magnification (Mo = di /do, with the minus sign omitted.)

Compound microscopes can have interchangeable eyepieces with magnifications from about 5 X to 100 X. Also, compound microscopes usually have rotating turrets that contain two or three different objectives for different magnifications.

Opaque objects (objects that do not let light pass through it) are usually illuminated with a light source placed above them. Specimens that are transparent are illuminated with a light source beneath the microscope stage so that light passes through the specimen. A standard microscope usually has a light condenser (converging lens) and a diaphragm below the stage, which are used to concentrate the light and control its intensity.

Telescopes

There are three different telescopes discussed in this section:

Refracting Telescope, Astronomical Telescope, Terrestrial Telescope

Telescopes have greatly advanced the field of astronomy and optics since their early development by Galileo Galilee in 1600. With the advent of Issac Newton's home-made metal mirror and Leon Foucault's developement of the glass mirror in 1856, the evolution of the telescope mirror has steadily progressed to its present state. With more perfect reflective surfaces came higher accuracies of the telescope. Telescopes apply the optical principles of mirrors and lenses to improve our abilities to see distant objects. Telescopes allow some objects to be viewed in greater detail and other more distant objects to be seen. In this section we will discuss the two basic types of telescopes: refracting and reflecting.

Refracting Telescope

The two major components of this type of telescope are a large converging objective lens with a long focal length, and the movable eyepiece has a relatively short focal length compared to the objective. Rays from a distant object are essentially parallel and form an image (Io) at the focal point (Fo) of the objective. The image acts as an object for the eyepiece, which is moved until the image lies just inside its focal point (Fe). A large, inverted, virtual image (Ie) is seen by the observer.

The magnifying power of a telescope focused for the final image at infinity can be shown to be:

Where the minus is inserted to indicate the image is inverted as in the lens sign convention. To achieve the greatest magnification, the focal length of the object should be made as great as possible and the focal length of the eyepiece as short as possible.

To produce upright images through terrestrial telescopes, there are two methods that are demostrated by the Galilean telescope and the erecting telescope.

A Galilean telescope, named after its creator who developed it in 1609, refers to a type of terrestrial telescope that has diverging lens used as an eyepiece. The light ryas pass through the eyepiece before the image is formed, and the image acts as a virtual object for the eyepiece. The observer sees a magnified, upright, virtual image. Galilean telescopes have a few disadvantages, such as the narrow fields of view and limited magnification.

Another telescope, the erecting telescope, uses a third lens, rightfully called the erecting lens, between converging objective and eyepiece lenses. If the image is formed by the objective at a distance that s twice the focal length of the intermediate erecting lens (2fi), then the lens merey inverts the image without magnifying it. However, this method to create an upright image requires a great telescope length (much greater than the Galilean telescope needs). Actually, the length of the telescope is increased by four times the focal length of the erecting lens. Nevertheless, the cumbersome length that it requires can be avoided by using internally reflecting prisms.

Reflecting Telescope

The intensity of light from a distant source is very weak. Intensity is energey per unit time per area. Thus, the more light can be gathered if the size of the objective is increased. This in turn increases the distance at which the telescope can detect faint objects such as a distant star or galaxy. However, due to the difficulties of producing large lenses (glass quality is most definitely inversely proportional to the size of the lens), we depend on compound lens systems to reduce aberrations.

Fun Fact #1: The largest objective lens in use is part of a refracting telescope of the Yerkes Observatory at Williams Bay, Wisconsin. It has a diameter of 40 inches (102 cm).

Fun Fact #2: The largest single-mirrored telescope was the Hale Observatories reflecting telescope, on Palomar Mountain in California, with a mirror 5.1 meters (200 inches) in diameter.

A reflecting telescope uses a large, concave, front-surface parabolic mirror. A parabolic mirror does not exhibit spherical abberation, and a mirror has no inherent chromatic abberation.

Even though reflecting telescopes have some advantages over refracting telescopes, they also have their own troubles. Like a large lens, a large mirror can sag under its massiveness. Also, the cost of a reflecting telescope is very high considering the supporting elements needed for a heavy mirror. Scientists are trying to solve these problems by using several small mirrors in place of just one large one. For example, the twin Keck telescopes at Mauna Kea in Hawaii is has a mirror consisting of 36 hexagonal segments that are computerized to give the effect of a 10-meter mirror.

Diffraction and Resolution

Resolution, Rayleigh criterion

The diffraction of light limits our ability to distinguish objects that are close together when we use microscopes or telescopes. This effect can be understood by considering two point sources located far from a narrow slit of width d. The sources could be two stars in the sky. When there is no diffraction, two bright spots would be observed on a screen. The slit diffracts light, and each image consists of a central maximum with a pattern of weaker bright and dark fringes on either side. If the sources are close together, the two central maxima may overlap. If this happens, the images cannot be resolved.

In general, images of two sources can be resolved if the central maximum of one falls at or beyond the first minimum (dark fringes) of the other (as stated in the Rayleigh criterion).

Besides the definition of the Rayleigh criterion above, it can also be expressed in terms of angular separation of the sources. The first minimum (m = 1) for a single-slit diffraction pattern satisfies this relationship:

This equation give the minimum angular separation for two images to be just resolved according to the Rayleigh criterion.

Back Home :: Back to Top
Lessons :: Terms :: Formulas :: Discuss :: Links