Ch 24. Geometric Optics

Transcription

1 text concept Ch 24. Geometric Optics Fig A point source of light P and its image P, in a plane mirror. Angle of incidence =angle of reflection.

2 text. Fig The blue dashed line through object point P is perpendicular to the plane of a mirror. The extension of any reflected light ray behind the mirror intersects this line at a point P. Because the angle of reflection equals the angle of incidence, P is the same distance d from the mirror plane as the object point. This conclusion is valid for any light ray at any angle of incidence. Thus all reflected rays appear to be coming from P Fig Observer O sees the image at point P, but observer O does not see the image.

3 text Ex-1.

4 text. Fig (a) A concave mirror. (b) A convex mirror. (a) Parallel rays from a distant point source are reflected by a concave mirror and converge to form a real image. The distant object point is on the optical axis, a line perpendicular to the center of the reflecting surface. The image point F is called the focal point. The distance f from the mirror to the focal point is called the focal length. The center of curvature C is the center of the spherical reflecting surface.

5 text. (b) A point object at P a distance s from the mirror produces a real image at P a distance s from the mirror. In this drawing the incident and reflected rays at the top of the mirror make a smaller angle than in the preceding drawing. The object is closer to the mirror and the image is farther away than in (a).

6 text. (c) The object P is at the same point occupied by the image in (b). Therefore the incident rays are just the reverse of the reflected rays in (b). The law of reflection then predicts that the reflected rays here will be the reverse of the former incident rays. The paths of the rays in both figures are the same, but the directions of the rays are opposite. This means that object and image points are interchanged. This result is an example of a general principle, the principle of optical reversibility: One may always interchange an object and an image, reversing the directions of all rays. This principle applies to both reflection and refraction and follows from the fact that the laws of reflection and refraction do not involve the direction of light rays.

7 text. (d) The object is placed at the focal point F. Applying the principle of optical reversibility to (a), where F was an image point, we find that the image here is at infinity, the location of the object point in (a). (e) When the object is placed inside the focal point, the incident and reflected rays form larger angles, and the reflected rays no longer intersect. Instead the reflected rays diverge from a point P behind the mirror, forming a virtual image as in the case of a plane mirror.

8 text Fig Light rays diverging from object. point P are reflected from a concave mirror and converge at image point P. The image distance s depends on the object distance s and on the mirror s radius of curvature. Fig Exterior angle '4 equals the sum of the two opposite interior angles, '1 and '2.

9 text concept Ch 24. Geometric Optics

10 text concept.

11 text.spherical mirror. Fig (a) Rays from a distant point source on the optical axis are incident on a spherical mirror. Only paraxial rays converge at the focal point. (b) For a parabolic mirror all rays from a distant point source on the optical axis converge at the focal point.

12 text. Fig A virtual object point P. Light rays converging toward P are interrupted by a mirror before reaching that point. Fig Derivation of an equation to locate the virtual image formed by a concave mirror when an object is inside the mirror s focal point. If we take the image distance s to be negative, we obtain the same equation used for a real image.

13 text. Fig (a) A lens forms a real image. (b) A concave mirror is placed in front of the image, which then serves as a virtual object for the mirror. The mirror image of this object is formed in front of the mirror.

14 text. Fig Image formation by a convex mirror.

15 text. Fig When a mirror image is farther from the mirror than the object, it is also larger than the object. Fig Linear magnification by a concave mirror: the image PQ is larger than the object PQ.

16 text Ex-3.

17 Concave text mirrors. Real object, real image Convex mirrors Real object, virtual image NOT POSSIBLE Real object, virtual image Virtual object, virtual image

18 text Ex-4.

19 text Ex-5.

20 text (a) Convex converging surface. (b) Concave converging surface (c) Concave diverging surface (d) Convex diverging surface Fig Determination of a surface as converging or diverging follows from the rule that rays transmitted into a higher-index medium bend toward the normal, and rays transmitted into a lower-index medium bend away from the normal.

21 text concept.

22 text concept.

23 text.lens. (b) Converging lens (a) Converging lens (d) Diverging lens (c) Diverging lens Fig Spherical lenses.

24 text. Fig Refraction at a spherical surface produces an image at P of an object at P

25 text Ex-6.

26 text. Fig The image formed by a lens s first surface serves as an object for its second surface.

27 text. Fig Image formation by a positive lens. A point object on the optical axis is at a great distance in (a) and is closer to the lens in each successive illustration. As the object comes closer, the image moves away. The principle of optical reversibility is illustrated by the interchange of objects and images in (a) and (d) and again in (b) and (c).

28 text. When an object is just outside the focal point of a positive lens, the distance from lens to image is much greater than the focal length. Fig Three lenses with progressively shorter focal lengths. A very short focal length, or high optical power, requires very small radii of curvature, which means a high power lens must be small. Fig Image formation by a negative lens.

29 text Ex-7.

30 text Ex-7.

31 text Ex-8.

32 text. Fig Derivation of the magnification equation for a real image of a real object. The ray striking the center of the lens passes straight through. This section of the lens is approximately like a flat, thin sheet of glass and, as seen in Example 4, Chapter 23, will not change the direction of the incident ray.

33 text Ex-9.

34 text Ex-9.

35 text. Fig The graphical method applied to positive and negative lenses.

36 text Ex-10.

37 text Ex-10.

38 text. Fig Chromatic aberration, illustrated in (a) and (b), is caused by dispersion of light in glass, a prismlike effect. The amount of dispersion depends on the kind of glass used for the lens. The negative lens in (b) uses a glass with greater dispersion (a larger variation in n) than the positive lens in (a), but because the shape of the negative lens results in less refraction (a longer focal length), the angular spread of the spectrum for the two lenses is the same. Thus combining the lenses, as shown in (c), results in a positive-focal-length lens, which displays no dispersion. Such a combination is called an achromatic doublet. Illustrations (a) and (b) show an exaggerated amount of dispersion, about 20 times that of typical glass.

39 text. Fig The distorted, multicolored image of graph paper seen through the lens is the result of chromatic and other aberrations. Fig Spherical aberration. Rays striking the lens near its edge have relatively large angles of incidence and refraction. Hence the small-angle approximation, used to obtain the thin-lens focal length, fails. These nonparaxial rays cross the optical axis inside the thin-lens focal point. Spherical aberration can be reduced by placing a screen with a small aperture in front of the lens so as to block rays near the edge of the lens.

40 text. Fig Light rays diverging from object point P are refracted by a convex spherical surface and converge at image point P. The image distance s depends on the object distance s, on the radius of curvature R, and on the refractive indices n and n

41 --- text.