. A text book of physics, for the use of students of science and engineering . FIG. 538.—Spherical refracting surface. It must be remembered that in Fig. 538 (a), rx is essentiallylegative, in accordance with the convention of signs. Again, wheni and r are small, we may, without sensible error, write sin % _ % _sin r r or Hence, BP u or BP H1 u I1 BP v -1 i = This gives the relation between u and v for a single spherical refract-ing surface. The equation is more complicated than for a sphericalmirror, and involves the refractive index of the medium, which itobviously must do. ;
. A text book of physics, for the use of students of science and engineering . FIG. 538.—Spherical refracting surface. It must be remembered that in Fig. 538 (a), rx is essentiallylegative, in accordance with the convention of signs. Again, wheni and r are small, we may, without sensible error, write sin % _ % _sin r r or Hence, BP u or BP H1 u I1 BP v -1 i = This gives the relation between u and v for a single spherical refract-ing surface. The equation is more complicated than for a sphericalmirror, and involves the refractive index of the medium, which itobviously must do. ; Expt. 127.—Refraction at a curved surface. Place a pin A (Fig. 5* (2)upright inside a glass crystallising basin containing water, fixing itmeans of soft wax. Let the basin rest upon a sheet of drawing paj 590 LIGHT CHAP. Fix two other pins at B and C, in line with the image I as seen by the fix other pairs of pins at DE, FG, etc. Mark the outline of the. Fig. -Refraction at a curved surface. basin on the paper and then remove it. Produce ED, CB, GF, etc., back-wards to meet at I. Taking IP as v, AP as u, and i\ as the radius of thebasin, calculate /x from the equation on p. 589. Note that rays far fromthe axis AG must not be taken, and further, that the thickness of the glass walls will prevent any greataccuracy being attained. Aplanatic surface.—There is one important case in which a spherical surface produces a true point image however large may be the beam employed. A surface which does this is called an aplanatic surface. Spherical surfaces as a rule are not aplanatic. Consider a sphere of glass of radius r =OC, having centre at O (Fig. 540). Draw also two circles having their centres at O, one having radius fxr and the other rjfu Thus BO = //>- and AO = r/fi, or BO/OC =--/*, and OC/AO = /x. Hence BO/OC=OC/OA, and the triangles BOC and COA, having the common angle at O, are similar, and -OBC = ^OCA. anu\gain, from trigonometr
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