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REFLECTION OF LIGHT
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REFLECTION OF See also:LIGHT . When a See also:ray of light in a homogeneous See also:medium fails upon the bounding See also:surface of another medium, See also:part of it is usually turned back or reflected and part is scattered, the See also:remainder traversing or being absorbed by the second medium. The scattered rays (also termed the irregularly or diffusely reflected rays) See also:play an important part in rendering See also:objects visible—in fact, without diffuse reflection non-luminous objects would be invisible; they are occasioned by irregularities in the surface, but are governed by the same See also:law as holds for See also:regular reflection. This law is: the incident and reflected rays make equal angles with the normal to the reflecting surface at the point of incidence, and are coplanar with the normal. This is See also:equivalent to saying that the path of the ray is a minimum.' In fig. i , MN represents the See also:section of a See also:plane See also:mirror; OR is the incident ray, RP the reflected ray, and TR the normal at R. Then the law states that the See also:angle of incidence ORT equals the angle of reflection PRT, and that M OR, RT and RP are in the same plane. This natural law is capable of ready experimental See also:proof (a See also:simple one is to take the See also:altitude of a See also:star with a See also:meridian circle, its depression in a See also:horizontal reflecting surface of See also:mercury and the direction of the See also:nadir), and the most delicate See also:instruments have failed to detect any divergence from it. Its explanation by the Newtonian corpuscular theory is very simple, for we have only to assume that at the point of impact the perpendicular velocity of a corpuscle is reversed, whilst the horizontal velocity is unchanged (the mirror being assumed horizontal). The See also:wave-theory explanation is more complicated, and in the simple See also:form given by See also:Huygens incomplete. The theory as See also:developed by See also:Fresnel shows that regular reflection is due to a small See also:zone in the neighbourhood of the point R (above), there being destructive interference at all other points on the mirror; this theory also accounts for the polarization of the reflected light when incident at a certain angle (see POLARIZATION OF LIGHT). The smoothness or See also:polish of the surface largely controls the reflecting See also:power, for, obviously, crests and furrows, if of sufficient magnitude, disturb the phase relations. The permissible deviation from smoothness depends on the wave-length of the light employed: it appears that surfaces smooth to within 8th of a wave-length reflect regularly; hence See also:long waves may be regularly reflected by a surface which diffuses See also:short waves. Also the obliquity of the incidence would diminish the effect of any irregularities; this is experimentally confirmed by observing the images produced by matt surfaces or by smoked See also:glass at grazing incidence. We now give some elementary constructions of reflected rays, or, what comes to the same thing, of images formed by mirrors. 1. If 0 be a luminous point and OR a ray incident at R on the plane mirror MN (fig. I) to determine the reflected ray and the See also:image of O. If RP be the reflected ray and RT perpendicular ' This principle of the minimum path, however, only holds for plane and See also:convex surfaces; with See also:concave surfaces it may be a maximum in certain cases. to MN, then, by the law of reflection, angle ORT=TRP or See also:ORM=PRN. Hence draw OQ perpendicular to MN, and produce it to S, making QS = OQ ; join SR and produce to P. It is easily seen that PR and OR are equally inclined to RT (or MN). A point-See also:eye at P would see a point See also:object 0 at S, i.e. at a distance below the mirror equal to its height above. If the object be a solid, then the images of its corners are formed by taking points at the same distances below as the corners are above the mirror, and joining these points. The eye, however, See also:sees the image perverted, i.e., in the same relation as the . 2. See also:left See also:hand to the 2. If A, B be two parallel plane mirrors and 0 a luminous point between them (fig. 3) to determine the images of 0 all the images must he on the See also:line (produced) PQ passing through 0 and perpendicular to the mirrors. Let OP = p, OQ = q. the image of 0 in A, 00'=2p; now 0' has an image 0" in B, such that 00"=OQ+QO"=q+q+2p=2p+2q; similarly 0" has an image O"' in A, such that 00"'=4p+2q. In the same way 0 forms an image 01 in B such that OOI =2q; OI has an image On in A, such that OOii=2p+2q; On has an image 0111 in B, such that OOiu=2p+4q, and so on. Hence there are an See also:infinite number of images at definite distances from the mirrors. This explains the vistas as seen, for example, between two parallel mirrors at the ends of a See also:room. 3. If A, B be two plane mirrors inclined at an angle 0, and intersecting at C, and 0 a luminous point between them, determine the position and number of images. See also:Call arc OA=a, OB=$. The image of 0 in A, i.e. a', is such that Oa' is perpendicular to CA, and Oa' =2a. Also Ca' = CO ; and it is easily seen that all the images See also:lie on a circle of centre C and See also:radius CO. The image a' forms an image a" in B such that Oa" =OB+Ba"=$+Ba'=p+OB+Oa'=210 +2a=20. Also a" forms an image a"' in A such that Oa' =OA+Aa'=2a+2B. And generally Oats=2ne, Oa2rt1=2n0+2a. In the same way it can be shown that the image first formed in B gives foci of the See also:general distances: Ob2°=2110, Ob2s+'=2ne+2$. The number of images is limited, for when any one falls on the arc ab between the mirrors produced, it lies behind both mirrors, and hence no further image is possible. Suppose a=s be the first image to fall on this arc, then arc Oa2s> OBa, i.e. 2n9> 1r—a or 2n> (,r-a)/0. Similarly if See also:a2" 1 be the first to fall on ab, we obtain 2n+I> (r—a)/0. Hence in both cases the number of images is the integer next greater than (r—a)/0. In the same way it can be shown that the number of images of the b See also:series is the integer next greater than (ir—$)/B. If 1r/8 be an integer, then the number of images of each series is ,r/B, for a/0 and $/0 are proper fractions. But an image of each series coincides; for if r/0=2n, we have 0a2n+0b2s=2ne+2ne=2,r i.e. a2n and b2s coincide; and if it/0=2n+I, we have See also:Dais+'+ Obent14nb+2 (a+0) _ (4n+2) 0= 2r, i.e. a2n+' and See also:ben+' coincide. Hence the number of images, including the luminous point, is 2er/0. This principle is utilized in the See also:kaleidoscope (q.v.), which produces five images by meahs of its mirrors inclined at 6o° (fig. 4). Fig. 5 shows the seven images formed by mirrors inclined at 45°. 4. To determine the reflection at a spherical surface. Let APB (fig. 6) be a section of a concave spherical mirror through its centre 0 and luminous point U. If a ray, say UP, meet the surface, it will be reflected along PV, which is coplanar with UP and the normal PO at P, and makes the angle VPO = UPO. Hence VO/VP=OU/UP. This expression may be simplified if we assume P to be very See also:close to A, i.e. that the ray UP is very slightly inclined to the See also:axis. See also:Writing A for P, we have VO/AV=OU/AU; and calling AU=u, AV=v and AO=r, this reduces to u-'+v-'=2r'. This See also:formula connects the distances of the object and image formed by a spherical concave mirror with the radius of the mirror. Points satisfying this relation are called " conjugate foci," for obviously they are reciprocal, i.e. u and v can be interchanged in the formula. ]~'IG. 4" FIG. S. If u be infinite, as, for example, if the luminous source-,be a star, then v-' =2r-', i.e. v = ir. This value is called the See also:focal length of the mirror, and the corresponding point, usually denoted by F, is called the " See also:principal See also:focus." This formula requires modification for a convex mirror. If u be always considered as See also:positive (v may be either positive or negative), r must be regarded as positive with concave mirrors and negative with convex. Similarly the focal length, having the same sign as r, has different signs in the two cases. In this formula all distances are measured from the mirror; but it is sometimes more convenient to measure from the principal focus. If the distances of the object and image from the principal focus be x and y, then u=x-{-f and v=y-{-f (remembering that f is positive for concave and negative for convex mirrors). Substituting these values in u-'+ir'= f-' and reducing we obtain xy =See also:f2. Since f2 is always positive, x and y must have the same sign, i.e. the object and image must lie on the same See also:side of the principal focus. We now consider the See also:production of the image of a small object placed symmetrically and perpendicular to the axis of a concave (fig. y) and a convex mirror (fig. 8). Let PQ be the object and A A Qt" the vertex of the mirror. ,Consider the point P. Now a ray through P and parallel to the axis after See also:meeting the mirror at M is reflected through the focus F. The line MF must therefore contain the image of P. Also a ray through P and also through the centre of curvature C of the mirror is reflected along the same path ; this also contains the image of P. Hence the image is at P, the intersection of the lines MF and PC. Similarly the image of any other point can be found, and the final image deduced. We See also:notice that in fig. 6 the image is inverted and real, and in fig. 7 erect and virtual. The " magnification " or ratio of the See also:size of the image to the object can be deduced from the figures by elementary See also:geometry; it equals the ratio of the distances of the image and object from the mirror or from the centre of curvature of the mirror. The positions and characters of the images for objects at varying O" O" QI q ?" distances are shown in the table (F is the principal focus and C the centre of curvature of the mirror MA). Additional information and CommentsThere are no comments yet for this article.
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