Lenses and Mirrors Help (page 2)
Introduction to Lenses and Mirrors—The Convex Lens
The ways in which visible light is reflected and refracted can be used to advantage. This was first discovered when experimenters noticed that specially shaped pieces of glass could make objects look larger or smaller. The refractive properties of glass have been used for centuries to help correct nearsightedness and farsightedness. Lenses work because they refract light more or less depending on where and at what angle the light strikes their surfaces. Curved mirrors have much the same effect when they reflect light.
The Convex Lens
You can buy a convex lens in almost any novelty store or department store. In a good hobby store you should be able to find a magnifying glass up to 10 cm (4 in) or even 15 cm (6 in) in diameter. The term convex arises from the fact that one or both faces of the glass bulge outward at the center. A convex lens is sometimes called a converging lens . It brings parallel light rays to a sharp focus or focal point , as shown in Fig. 17-4 A , when those rays are parallel to the axis of the lens. It also can collimate (make parallel) the light from a point source, as shown in Fig. 17-4 B .
The properties of a convex lens depend on the diameter of the lens, as well as on the difference in thickness between the edges and the center. The larger the diameter, the greater is the light-gathering power. The greater the difference in thickness between the center and the edges, the shorter is the distance between the lens and the point at which it brings parallel light rays to a focus. The effective area of the lens, measured in a plane perpendicular to the axis, is known as the light-gathering area . The distance between the center of the lens and the focal point (as shown in Fig. 17-4 A or B ) is called the focal length . If you look through a convex lens at a close-up object such as a coin, the features are magnified; they appear larger than they look with the unaided eye.
The surfaces of convex lenses generally are spherical. This means that if you could find a large ball having just the right diameter, the curve of the lens face would fit neatly inside the ball. Some convex lenses have the same radius of curvature on each face; others have different radii of curvature on their two faces. Some converging lenses have one flat face; these are called planoconvex lenses .
The Concave Lens
You will have some trouble finding a concave lens in a department store, but you should be able to order them from specialty catalogs or Web sites. The term concave refers to the fact that one or both faces of the glass bulge inward at the center. This type of lens is also called a diverging lens . It spreads parallel light rays outward (Fig. 17-5 A ). It can collimate converging rays if the convergence angle is correct (see Fig. 17-5 B ).
As with convex lenses, the properties of a concave lens depend on the diameter and the extent to which the surface(s) depart from flat. The greater the difference in thickness between the edges and the center of the lens, the more the lens will cause parallel rays of light to diverge. If you look through a concave lens at a close-in object such as a coin, the features are reduced; they appear smaller than they look with the unaided eye.
The surfaces of concave lenses, like those of their convex counterparts, generally are spherical. Some concave lenses have the same radius of curvature on each face; others have different radii of curvature on their two faces. Some diverging lenses have one flat face; these are called planoconcave lenses .
The Convex Mirror
A convex mirror reflects light rays in such a way that the effect is similar to that of a concave lens. Incident rays, when parallel, are spread out (Fig. 17-6 A ) after they are reflected from the surface. Converging incident rays, if the angle of convergence is just right, are collimated by a convex mirror (see Fig. 17-6 B ). When you look at the reflection of a scene in a convex mirror, the objects all appear reduced. The field of vision is enlarged, a fact that is used to advantage in some automotive rear-view mirrors.
The extent to which a convex lens spreads light rays depends on the radius of curvature. The smaller the radius of curvature, the greater is the extent to which parallel incident rays diverge after reflection.
The Concave Mirror
A concave mirror reflects light rays in a manner similar to the way a convex lens refracts them. When incident rays are parallel to each other and to the axis of the mirror, they are reflected so that they converge at a focal point (Fig. 17-7 A ). When a point source of light is placed at the focal point, the concave mirror reflects the rays so that they emerge parallel (see Fig. 17-7 B ).
The properties of a concave mirror depend on the size of the reflecting surface, as well as on the radius of curvature. The larger the light-gathering area, the greater is the light-gathering power. The smaller the radius of curvature, the shorter is the focal length. If you look at your reflection in a convex mirror, you will see the same effect that you would observe if you placed a convex lens up against a flat mirror.
Concave mirrors can have spherical surfaces, but the finest mirrors have surfaces that follow the contour of an idealized three-dimensional figure called a paraboloid . A paraboloid results from the rotation of a parabola, such as that having the equation y = x 2 in rectangular coordinates, around its axis. When the radius of curvature is large compared with the size of the reflecting surface, the difference between a spherical mirror and a paraboloidal mirror (more commonly called a parabolic mirror ) is not noticeable to the casual observer. However, it makes a big difference when the mirror is used in a telescope.
Practice problems of this concept can be found at: Optics and Telescopes Practice Problems
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