33.0 - Introduction
Lenses may be the application of refraction with which you are most familiar.
Lenses of glass or plastic, fashioned into eyeglasses and contact lenses, are worn
by about 60% of the population of the United States, and this percentage is
projected to increase as the population ages. Even people who do not require visual
correction are “wearing” lenses anyway, since the eye itself contains an organic
lens.
The human eye has the ability to refract light and focus it on the retina at the back of
the eye, where signals are then transmitted to the brain. If the focusing is not
precise enough, glasses or contact lenses can improve the results. These days, the
eye itself can be tuned via laser surgery as well.
Lenses augment vision in other fashions as well. Lenses in magnifying glasses,
telescopes, and microscopes allow you to see things that would otherwise be too
small or too far away to see in detail.
At the right, you can begin your experimentation with lenses. The convex lens will
produce an image of the penguin. You can move the penguin left and right to see
how its distance from the lens changes the resulting image. Where must the object be relative to the focal point F to create an image on the
same side of the lens as the object? Where must it be to create an image on the far side? Can you make the image appear right-side up (rather
than inverted, as it is in the picture on the right)? A note: When the object is very near the focal point, the image will be too far away from the
lens to be shown in the simulation’s window.
33.1 - Lenses
Lens: A device that uses
refraction to redirect and
focus light.
Light changes direction í refracts í as it passes from
air to a lens material and back to air. Lenses take
advantage of refraction to create images.
In general, lenses are made of a transparent material
with a curved surface or surfaces. Although lenses
are typically curved, we will use two prisms, as shown
to the right, to introduce the fundamental functioning of lenses.
In the upper diagram, you see two prisms placed so that their flat bases are touching.
Three parallel rays of light strike the prisms. Because of the sloping surfaces of the
prisms, the rays are refracted in different directions.
As you can see, after passing through the prisms, the three rays converge on the far
side. This first set of prisms serves as a model for a converging lens. Converging lenses
are thickest at their centers. With a two-prism lens, all the incoming rays would not
converge at one point like the three we have chosen to show, which is why prisms do
not make good lenses: The image they create will be blurry. A curved surface will focus
the rays more precisely.
In the second diagram, we invert the prisms, so they touch tip to tip. The rays diverge
after passing through them; they will not intersect on the far side of the prisms. This
configuration provides a model for a diverging lens. The image created by a diverging
lens is a virtual one. By extending the paths of the rays that have passed through the
prisms backwards, we could locate the virtual image on the same side of the lens as the
object that creates it.
In this chapter, we focus on lenses that are both spherical and thin. A spherical lens has
two surfaces, each of which is a section of a sphere. The curvatures of the two sides of a lens can differ. Saying it is “thin” means the distance
across a lens is small relative to the distance to the object that is the source of the image. Thin lenses provide an accurate model for optical
equipment ranging from contact lenses to telescopes.
Much of the terminology and many basic concepts coincide for mirrors and lenses. A line that passes through the center of a lens
perpendicular to its surface is called the principal axis. Parallel rays from an object infinitely far away refract through a lens and converge at the
lens’s focal point. The focal lengthfis the distance between the lens’s center and its focal point. In contrast to mirrors, lenses have two focal
points, one on each side of the lens, since incident rays can originate on either side of a lens. Rays that are close to the principal axis and
Lenses are used in eyeglasses to focus images.Converging lens
Two stacked prisms form crude lens
Prisms refract light
Thicker at center