Topics in..
. Chemical Instrumentation
Edited by S. Z . LEWIN, N e w York University, New York 3, N. Y. is the refractive index of the lens, then the equation describing the rerpective distances is:
aufhms, are infended lo serue ihe read& of this J O ~ N A by L calling ah& lo new developments in the theow, desian,or auailabililv of chemical laboratmu instrumenla&, or by present& usad inn& and-e&lanations of top& that are of practical importance to Ucose who use, or leach the w e of, modern instrumentation and i&rumental techniques.
XXIV. lnstrumentation for Micrometry and Microscopy-Part
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5. Z . Lewin, Dept. o f Chemistry, N e w York University, N. Y . 3, N. Y. Simple rnsgnifiers of various kindfi have probably been made purposeful use of for more than three thousand years. I n the ancient near esst, glass globes filled with water may have been used by engravers as an aid in their carving of cylinder seals and similar artiiacts. Spheres of rock crystal were made by the ancients and may have served a similar purpose. The use of magnifying lenses for reading had already become common in the time of the Roman empire, and by the end of the sixteenth century in Europe, lens grinding was a well established and advanced art. The compound microscope was invented before the beginning of the seventeenth century, and its extensive use during that century was capped by the explanation of its theory given by Huygens in 1703. Yet, despite this venerable record of utilization and investigation of optical magnifying devices, fundament.dly new advances continue to be made in the design and application of this class of inst,rumentation. I t is sobering to reflect that, although the role of diffraction and interference phenomena in microscopy was well underst,ood as early as 1873 (and employed then by Abbe to develnp the concept of resolving power and numerical aperture), it wits more than 60 years later that Zernike hit upon the idea of inserting a simple shield over the light source, and a thin film over tho objective, to exploit inlerfcrenee in a manner that so improves the miermcopic image as t,o give birth to a, new field of mirlnsopy (viz., phase microscopy) and to win for himself a Nobel Prize (in 1953). The very considerable time lrtg between t,he instmment,al developments of Abbe and Zernike is B convequence of the remarkable subtlet,y and complexity of optical phenomena. The nature of light is st,ill but dimly understood, and many dramatic and powerful new applie%tions are doubtless in the offing.
Thus, il cen be see)! that ii the ohjerl, is small, sud is on the principal axis at. infinity (i.e., so far t o the left of the lens center thet the rays coming from it rxn all be assumed to be parallel to the prineipal axis) the rays will came to R focus at S, = I / [ ( n - 1) (]/XI l/Rz)l. If, ss i r t t h e usual case, both radii are equal and n = 1.5, this reduces t,o S- = R. The closer the ohjert romes to the lens, i.e., the srnaller S, becomes, t,he larger must Sxbe; i.e., t,he farther away from the lens is the image formed. If the object is located at S, = R, the image is formed a t infinity, k . , no image is formed. Thus, a real (and inverted) image is formed on1.v for objects located between the limits R and iufinity from t,he lens eent,er.
Types of Magnifiers The purpose of optical magnifiers is to present to the eye an image that is more readily perceived and amenable to me=urement or study than the image which the unaided eye is capable of forming. The magnifier may be designed to produce an image upon the retinal surfece of the observer's eye, in which case it is a visual inst,rument, or it may be devised to create an image on a photographic plate, a cathode ray tube, or a. viewing screen, in which case it is a projection instrument. The fiimplest magnifiers provide a single stage of ampli$catim, i.e., there is a single lens system which forms an image of the object, under study. Examples of such devices are the so-called reading glass, hand lens, pocket magnifier, loupe, and the "simple" microscope (as differentiated from the compound, or two stages of amplification, microscope). The most common form of these mamitiers eonsiste of & biconvex lens in a suitable mounting, and map be found in a variety of sizes and shapes, as illust,rated in Figure 1 , A-c.
The Biconvex Lens These lenses have spherical shapes, i.e., their surfaces are portionfi of spheres, as shown in Figure 2. The relationshipa bbetween the lorations and relative sizes of t,he ohject and irnsge are shown in the usual idealized wa,v in tllis figure. That, is, the rorresponcfing "oink of ohjert and
6)
the focal point in the i&gespare, and a ray fmm the object, through the center of the lens, which cont,inues on wit,hout, deviation. I f R, and R are t,he radii of curvature of t,he t,wo sides of the lens, S, is the distance of the ohject from the center of the lens (XO), S2is the distance of the image from the center (OY), and n
The lateral mapifieation is defined as the ratio of corresponding lateral (i.e., perpendicular to the principal axis) dimensions in the image and object respectively. From a comparison of similar triangles in Figure 2, i t will be seen that:
The relationship between St, SBand R given above permits us to rewrite this equation in the form:
which shows that the lateral magnification approaches infinity as the image approaches R (while, as seen above, the image location also approaches infinity). When S, = d R, M = 1. Hence, for lateral magnifications in excess of I X , (.he object must be closer to the lens than twice the radius of curvature. If S, is greeter than d R, the image is reduced. If the object is placed closer to the lens than R, a virlual, erect and enlarged image is farmed, as shown in Figure 3. This imago is virtual beeau~ethe rnys are divergent, and the image is seen only as a, rcaull of (.he ment,al ext,rapolation of these rays by the observer back toward the point, from which they appear to came. The general rel&tionships between the location of the object vis-a-vis the lens eent,er and the type of image formed are summarized graphically in Figure 4. When a biconvex lens is used as a reading glass, hand lens, or loupe, i t is usually this virtual image that is viewed. The (Conlinued on page A.566)
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Fig. 2. The chorocterirticr of the ordinary convex l e n s G,CZ: the centers of curvature of the two spherical rurfocer. PP: principal axis of the lenr. 0: Optical center of the lens. V,, VZ: vvenices of the lenr. h,F2: f0c.1 poinn. X,X: object. Y,Y: image [magnified and inverted). V. I.R . .T. I-I .A.I.
IMAGE PLANE
OBJECT
PLANE
Figure 3. Formation of virtual, erect, enlarged image when object i s closer to biconvex lens than the focal distance.
i
I
I
I
OBJECT
0
Fig. 1. A. Typical biconvex lens reading B. Pocket glasses (Edroy Products Co.. N. Y.1. mognifiem of the ~ i m p l ebiconvex lenr type. C. Watchmakers' loupe, of the simple biconvex lenr type.
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I
a
A
A
OBJECT
C
Figure 4. Schomotic rapresentalion of the relofive dinensionr o f imoge and object as a function of the location of the obiect with respect to the lenr. The lacotion of the image i s not represented in lhe diagmm. When the object is beyond the focal point, the image is r e d and inverted. When the object is beforethe focal point,theimogei$virtual and erect. (Catinued o n page A688)
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