Lenses Quiz

PDF page 527: aberration a distortion in an image produced by a lens angle of incidence the angle, with respect to the normal, at which a ray meets a boundary between media or a reflective surface angle of reflection the angle, with respect to the normal, at which a ray leaves a reflective surface angle of refraction the angle between the normal and the refracted ray central axis a line perpendicular to the center of a lens or mirror extending in both directions chromatic aberration an aberration related to color concave lens a lens that causes light rays to diverge from the central axis concave mirror a mirror with a reflective side that is curved inward converging lens a convex lens convex lens a lens that causes light rays to converge toward the central axis convex mirror a mirror with a reflective side that is curved outward critical angle an incident angle that produces an angle of refraction of 90° dispersion separation of white light into its component wavelengths diverging lens a concave lens focal length the distance from the focal point to the mirror

PDF page 513: the figure is the axis of the lens). The concave lens is a diverging lens because it causes the light rays to bend away (diverge) from its axis. In this case, the lens has been shaped so all light rays entering it parallel to its axis appear to originate from the same point, F, defined to be the focal point of a diverging lens. The distance from the center of the lens to the focal point is again called the focal length, or “ƒ,” of the lens. Note that the focal length of a diverging lens is defined to be negative. An expanded view of the path of one ray through the lens is shown in Figure 16.26 to illustrate how the shape of the lens, together with the law of refraction, causes the ray to follow its particular path and diverge.

PDF page 527: aberration a distortion in an image produced by a lens angle of incidence the angle, with respect to the normal, at which a ray meets a boundary between media or a reflective surface angle of reflection the angle, with respect to the normal, at which a ray leaves a reflective surface angle of refraction the angle between the normal and the refracted ray central axis a line perpendicular to the center of a lens or mirror extending in both directions chromatic aberration an aberration related to color concave lens a lens that causes light rays to diverge from the central axis concave mirror a mirror with a reflective side that is curved inward converging lens a convex lens convex lens a lens that causes light rays to converge toward the central axis convex mirror a mirror with a reflective side that is curved outward critical angle an incident angle that produces an angle of refraction of 90° dispersion separation of white light into its component wavelengths diverging lens a concave lens focal length the distance from the focal point to the mirror

PDF page 512: Lenses are found in a huge array of optical instruments, ranging from a simple magnifying glass to the eye to a camera’s zoom lens. In this section, we use the law of refraction to explore the properties of lenses and how they form images. Some of what we learned in the earlier discussion of curved mirrors also applies to the study of lenses. Concave, convex, focal point F, and focal length f have the same meanings as before, except each measurement is made from the center of the lens instead of the surface of the mirror. The convex lens shown in Figure 16.25 has been shaped so that all light rays that enter it parallel to its central axis cross one another at a single point on the opposite side of the lens. The central axis, or axis, is defined to be a line normal to the lens at its center. Such a lens is called a converging lens because of the converging effect it has on light rays. An expanded view of the path of one ray through the lens is shown in Figure 16.25 to illustrate how the ray changes

PDF page 513: the figure is the axis of the lens). The concave lens is a diverging lens because it causes the light rays to bend away (diverge) from its axis. In this case, the lens has been shaped so all light rays entering it parallel to its axis appear to originate from the same point, F, defined to be the focal point of a diverging lens. The distance from the center of the lens to the focal point is again called the focal length, or “ƒ,” of the lens. Note that the focal length of a diverging lens is defined to be negative. An expanded view of the path of one ray through the lens is shown in Figure 16.26 to illustrate how the shape of the lens, together with the law of refraction, causes the ray to follow its particular path and diverge.

PDF page 513: the figure is the axis of the lens). The concave lens is a diverging lens because it causes the light rays to bend away (diverge) from its axis. In this case, the lens has been shaped so all light rays entering it parallel to its axis appear to originate from the same point, F, defined to be the focal point of a diverging lens. The distance from the center of the lens to the focal point is again called the focal length, or “ƒ,” of the lens. Note that the focal length of a diverging lens is defined to be negative. An expanded view of the path of one ray through the lens is shown in Figure 16.26 to illustrate how the shape of the lens, together with the law of refraction, causes the ray to follow its particular path and diverge.

PDF page 513: Figure 16.26 Rays of light enter a concave, or diverging, lens parallel to its axis diverge and thus appear to originate from its focal point, F.

PDF page 513: The dashed lines are not rays; they indicate the directions from which the rays appear to come. The focal length, ƒ, of a diverging lens is negative. An expanded view of the path taken by ray 1 shows the perpendiculars and the angles of incidence and refraction at both surfaces. The power, P, of a lens is very easy to calculate. It is simply the reciprocal of the focal length, expressed in meters

PDF page 513: The units of power are diopters, D, which are expressed in reciprocal meters. If the focal length is negative, as it is for the diverging lens in Figure 16.26, then the power is also negative. In some circumstances, a lens forms an image at an obvious location, such as when a movie projector casts an image onto a screen. In other cases, the image location is less obvious. Where, for example, is the image formed by eyeglasses? We use ray

PDF page 514: 3. A ray passing through the center of either a converging or a diverging lens does not change direction

PDF page 514: 4. A ray entering a converging lens through its focal point exits parallel to its axis

PDF page 515: The image formed in Figure 16.27 is a real image—meaning, it can be projected. That is, light rays from one point on the object actually cross at the location of the image and can be projected onto a screen, a piece of film, or the retina of an eye. In Figure 16.27, the object distance, do, is greater than f. Now we consider a ray diagram for a convex lens where do< f, and another diagram for a concave lens.

PDF page 515: The image formed in Figure 16.27 is a real image—meaning, it can be projected. That is, light rays from one point on the object actually cross at the location of the image and can be projected onto a screen, a piece of film, or the retina of an eye. In Figure 16.27, the object distance, do, is greater than f. Now we consider a ray diagram for a convex lens where do< f, and another diagram for a concave lens.

PDF page 516: Real Positive Negative m >, <, or = ‒1 Case 1 f positive, do > f

PDF page 519: Real lenses behave somewhat differently from how they are modeled using rays diagrams or the thin-lens equations. Real lenses produce aberrations. An aberration is a distortion in an image. There are a variety of aberrations that result from lens size, material, thickness, and the position of the object. One common type of aberration is chromatic aberration, which is related to color. Because the index of refraction of lenses depends on color, or wavelength, images are produced at different places and with different magnifications for different colors. The law of reflection is independent of wavelength, so mirrors do not have this problem. This result is another advantage for the use of mirrors in optical systems such as telescopes.

PDF page 527: aberration a distortion in an image produced by a lens angle of incidence the angle, with respect to the normal, at which a ray meets a boundary between media or a reflective surface angle of reflection the angle, with respect to the normal, at which a ray leaves a reflective surface angle of refraction the angle between the normal and the refracted ray central axis a line perpendicular to the center of a lens or mirror extending in both directions chromatic aberration an aberration related to color concave lens a lens that causes light rays to diverge from the central axis concave mirror a mirror with a reflective side that is curved inward converging lens a convex lens convex lens a lens that causes light rays to converge toward the central axis convex mirror a mirror with a reflective side that is curved outward critical angle an incident angle that produces an angle of refraction of 90° dispersion separation of white light into its component wavelengths diverging lens a concave lens focal length the distance from the focal point to the mirror