OPTICAL INSTRUMENTS CHAPTER 19

Transcription

1 CHAPTER 9 OPTICAL INSTRUMENTS 9. THE EYE Opticl instruments re used primrily to ssist the eye in viewing n object. Let us first discuss in brief the construction of humn eye nd the mechnism by which we see, the most common but most importnt experiment we do from the dy we open our eyes. Figure (9.) shows schemticlly the bsic components of n eye. The eye hs nerly sphericl shpe of dimeter bout n inch. The front portion is more shrply- curved nd is covered by trnsprent protective membrne clled the corne. It is this portion which is visible from outside. Behin9I the corne, we hve spce filled with liquid clled the queous humor nd behind tht crystlline lens. Figure 9. Retin Between the queous humor nd the lens, we hve musculr diphrgm clled iris, which hs smll hole in it clled pupil. Iris is the coloured prt tht we see in n eye. The pupil ppers blck becuse ny 'light flling on it goes into the eye nd there is lmost no chnce of light coming bck to the outside. The mount of light entering the eye, my be controlled by vrying the perture of the pupil with the help of the iris. In low-light condition, the iris expnds the pupil to llow more light to go in. In good light conditions, it contrcts the pupil. The lens is hrd in the middle nd grdully becomes soft towrds the outer edge. The curvture of the lens my be ltered by the ciliry muscles to which it is ttched. The light entering the eye forms n imge on the retin which covers the inside of the rer prt of the eyebll. The retin contins bout 25 million receptors clled rods nd cones which receive the light signl nd bout one million optic-nerve fibres which trnsmit the informtion to the brin. The spce between the lens nd the retin is filled with nother liquid clled the vitreous humor. The queous humor nd the vitreous humor hve lmost sme refrctive index.336. The refrctive index of the mteril of the lens is different in different portions but on the verge it is bout.396. When light enters the eye from ir, most of the bending occurs t the corne itself becuse there is shrp chnge in the refrctive index. Some dditionl bending is done by the lens which is surrounded by fluid of somewht lower refrctive index. In norml conditions, the light should be focused on the retin. The corne-lens-fluid system is equivlent to single converging lens whose focl length my be djusted by the ciliry muscles. Now onwrds, we shll use the word eye-lens to men this equivlent lens. When the eye is focused on distnt object, the ciliry muscles re relxed so tht the focl length of the eye-lens hs its mximum vlue which is equl to its distnce from the retin. The prllel rys coming into the eye re then focused on the retin nd we see the object clerly. When the eye is focused on closer object, the ciliry muscles re strined nd the focl length of the eye-lens decreses. The ciliry muscles djust the focl length in such wy tht the imge is gin formed on the retin nd we see the object clerly. This process of djusting focl length is clled ccommodtion. However, the muscles cnnot be strined beyond limit nd hence, if the object is brought too close to the eye, the focl length cnnot be djusted to form the imge on the retin. Thus, there is minimum distnce for the cler vision of n object-

2 420 Concepts of Physics The nerest point for which the imge cn be focused on the retin, is clled the ner point of the eye. The distnce of the ner point from the eye is clled the lest distnce for cler vision. This vries from person to person nd with ge. At young ge (sy below 0 yers), the muscles re strong nd flexible nd cn ber more strin. The ner point my be s close s 7-8 cm t this ge. In old ge, the muscles cnnot sustin lrge strin nd the ner point shifts to lrge vlues, sy, to 2 m or even more. We shll discuss bout these defects of vision nd use of glsses in lter section. The verge vlue of the lest distnce for cler vision for norml eye is generlly tken to be 25 cm. 9.2 APPARENT SIZE The size of n object s sensed by us is relted to the size of the imge formed on the retin. A lrger imge on the retin ctivtes lrger number of rods nd cones ttched to it nd the object looks lrger. As is cler from figure (9.2), if n object is tken wy from the eye, the size of the imge on the retin decreses nd hence, the sme object looks smller. It is lso cler from figure (9.2) tht the size of the imge on the retin is roughly proportionl to the ngle subtended by the object on the eye. This ngle is known s the visul ngle nd opticl instruments re used to increse this ngle rtificilly in order to improve the clrity. h h Imge mge As ot, > 2, the first boy will look tller to the eye. 9.3 SIMPLE MICROSCOPE When we view n object with nked eyes, the object must be plced somewhere between infinity nd the ner point. The mximum ngle is subtended on the eye when the object is plced t the ner point. This ngle is (figure 9.3) 0 D where h is the size of the object nd D is the lest distnce for cler vision. h f () D F h (c) Figure 9.3 F--- f --I (b) This ngle cn be further incresed if converging lens of short focl length is plced just in front of the eye. When converging lens is used for this purpose, it is clled simple microscope or mgnifier. Suppose, the lens hs focl length f which is less thn D nd let us move the object to the first focl point F. The eye receives rys which seem to come from infinity (figure 9.3b). The ctul size of the imge is infinite but the ngle subtended on the lens (nd hence on the eye) is (i) Figure 9.2 e = Exmple 9. Two boys, one 52 inches tll nd the other 55 inches tll, re stnding t distnces 4.0 m nd 5.0 m respectively from n eye. Which boy will pper tller? Solution : The ngle subtended by the first boy on the eye is 52 inch 3 inch/m 4.0 m nd the ngle subtended by the second boy is 55 inch, = - incm. h/ 5.0m As f < D, equtions (i) nd (ii) show tht 0 > 00. Hence, the eye perceives lrger imge thn it could hve hd without the microscope. As the imge is situted t infinity, the ciliry muscles re lest strined to focus the finl imge on the retin. This sitution is known s norml djustment. We define mgnifying power of microscope s 0/00 where 0 is the ngle subtended by the imge on the eye when the microscope is used nd 00 is the ngle subtended on the nked eye when the object is plced t the ner point. This is lso known s the ngulr mgnifiction. Thus, the mgnifying power is the fctor by which the

3 Opticl Instruments 42 imge on the retin cn be enlrged by using the microscope. In norml djustment, the mgnifying power of simple microscope is, by (i) nd (ii), e h/ f m = - 0. VD D m= - f... (9.) the objective nd the one close to the eye is clled the eyepiece or oculr. The objective hs smller perture nd smller focl length thn those of the eyepiece. The seprtion between the objective nd the eyepiece cn be vried by pproprite screws fixed on the pnel of the microscope. Eyepiece If f < D, the mgnifying power is greter thn. The mgnifying power cn be further incresed by moving the object still closer to the lens. Suppose, we move the object to distnce uo from the lens such tht the virtul erect imge is formed t the ner point (figure 9.3c). Though the eye is strined, it cn still see the imge clerly. The distnce uo cn be clculted using the lens formul, =. u v f Here v = - D nd u = - uo, so tht - uo - 7 D uo D The ngle subtended by the imge on the lens (nd hence on the eye) is 0'= - uo The ngulr mgnifiction or mgnifying power in this cse is _ (3, h/uo m eo h/d D uo = +... (9.2) Equtions (9.) nd (9.2) show tht the mgnifiction cn be mde lrge by choosing the focl length f smll. However, due to severl other berrtions the imge becomes too defective t lrge mgnifiction with simple microscope. Roughly speking, mgnifiction upto 4 is trouble-free. The mgnifying power is written with unit X. Thus, if mgnifier produces n ngulr mgnifiction of 0, it is clled 0 X mgnifier. 9.4 COMPOUND MICROSCOPE (iii) Figure (9.4) shows simplified version of compound microscope nd the ry digrm for imge formtion. It consists of two converging lenses rrnged coxilly. The one fcing the object is clled Imge Figure 9.4 The object is plced t distnce uo from the objective which is slightly greter thn its focl length 0. A rel nd inverted imge is formed t distnce vo on the other side of the objective. This imge works s the object for the eyepiece. For norml djustment, the position of the eyepiece is so djusted tht the imge formed by the objective flls in the focl plne of the eyepiece. The finl imge is then formed t infinity. It is erect with respect to the first imge nd hence, inverted with respect to the object. The eye is lest strined in this djustment s it hs to focus the prllel rys coming to it. The position of the eyepiece cn lso be djusted in such wy tht the finl virtul imge is formed t the ner point. The ngulr mgnifiction is incresed in this cse. The ry digrm in figure (9.4) refers to this cse. In effect, the eyepiece cts s simple microscope used to view the first imge. Thus, the mgnifiction by compound microscope is two step process. In the first step, the objective produces mgnified imge of the given object. In the second step, the eyepiece produces n ngulr mgnifiction. The overll ngulr mgnifiction is the product of the two. Mgnifying power Refer to figure (9.4). If n object of height h is seen by the nked eye, the lrgest imge on the retin is formed when it is plced t the ner point. The ngle formed by the object on the eye in this sitution is e 0 = D (i)

4 - 422 Concepts of Physics When compound microscope is used, the finl imge subtends n ngle 0' on the eyepiece (nd hence on the eye) given by ' 6' = h (ii) ue where h' is the height of the first imge nd u, is its distnce from the eyepiece. The mgnifying power of the compound microscope is, therefore, m= = X = [[P_ Bo u, h h ue ] Also from figure (9.4), h' h vo v uo u Now, D/u, is the mgnifying power of the eyepiece treted s simple microscope. Using (9.) nd (9.2), this is equl to Dui, in norml djustment (imge t infinity) nd + D/f5 for the djustment when the imge is formed t the lest distnce for cler vision i.e., t D. Thus, the mgnifying power of the compound microscope is, by (iii), m = [D] u f, for norml djustment nd m = u [ + fe... (9.4) for the djustment when the finl imge is formed t the lest distnce for cler vision. Using lens eqution for the objective, v u f v v - = u fo v = _ 0 In generl, the focl length of the objective is very smll so tht L' >>. Also, the first imge is close to f o the eyepiece so tht v = where is the tube-length (seprtion between the objective nd the eyepiece). Thus, =- = u If these conditions re stisfied, the mgnifying power of the compound microscope is, by (9.3) nd (9.4), D m= fo fe for norml djustment nd m = - [ + fo (iii)... (iv)... (9.3) for djustment for the finl imge t the lest distnce for cler vision. In n ctul compound microscope ech of the objective nd the eyepiece consists of combintion of severl lenses insted of single lens s ssumed in the simplified version. Exmple 9.2 A compound microscope hs n objective of focl length cm nd n eyepiece of focl length 2.5 cm. An object hs to be plced t distnce of.2 cm wy from the objective for norml djustment. () Find the ngulr mgnifiction. (b) Find the length of the microscope tube. Solution : () If the first imge is formed t distnce v from the objective, we hve v (-.2 cm) cm v = 6 cm. The ngulr mgnifiction in norml djustment is D 6 cm 25 cm m u fe '2 cm 2'5 cm (b) For norml djustment, the first imge must be in the focl plne of the eyepiece. The length of the tube is, therefore, 9.5 TELESCOPES L = + fe = 6 cm + 2'5 cm = 8'5 cm. A microscope is used to view the objects plced close to it sy within few centimeters. To look t distnt objects such s str, plnet or distnt tree etc. we use nother instrument clled telescope. We shll describe three types of telescopes which re in use. (A) Astronomicl Telescope Figure (9.5) shows the construction nd working of simplified version of n stronomicl telescope.... _ Milnllki I b...= Il \IIII ' _-.willia ,-- -. t...,,,-.. Q" ,-,- _ _, Figure 9.5

5 Opticl Instruments 423 It consists of. two converging lenses plced coxilly. The one fcing the distnt object is clled the objective nd hs lrge perture nd lrge focl length. The other is clled the eyepiece, s the eye is plced close to it. It hs smller perture nd smller focl length. The lenses re fixed in tubes. The eyepiece tube cn slide within the objective tube so tht the seprtion between the objective nd the eyepiece my be chnged. When the telescope is directed towrds distnt object PQ, the objective forms rel imge of the object in its focl plne. If the point P is on the principl xis, the imge point P is t the second focus of the objective. The rys coming from Q re focused t Q'. The eyepiece forms mgnified virtul imge P"Q" of P. This imge is finlly seen by the eye. In norml djustment, the position is so djusted tht the finl imge is formed t infinity. In such cse, the first imge P'Q' is formed in the first focl plne of the eyepiece. The eye is lest strined to focus this finl imge. The imge cn be brought closer by pushing the eyepiece closer to the first imge. Mximum ngulr mgnifiction is produced when the finl imge is formed t the ner point. Mgnifying Power Suppose, the objective nd the eyepiece hve focl lengths fo nd f, respectively nd the object is situted t lrge distnce uo from the objective. The object PQ in figure (9.5) subtends n ngle on the objective. Since the object is fr wy, the ngle it would subtend on the eye, if there were no telescope, is lso essentilly. As uo is very lrge, the first imge P Q' is formed in the focl plne of the objective. From the figure, OP' P'Q' fo The finl imge Q" subtends n ngle p on the eyepiece (nd hence on the eye). We hve from the tringle P Q'E 3 I tn f3 I - EP fo (i) (ii) If the telescope is set for norml djustment so tht the finl imge is formed t infinity, the first imge P'Q' must be in the focl plne of the eyepiece. Then EP = fe. Thus, eqution (ii) becomes fo fe The ngulr mgnifiction or the mgnifying power of the telescope is defined s ngle subtended by the finl imge on the eye m - ngle subtended by the object on the unided eye The ngles p nd re formed on the opposite sides of the xis. Hence, their signs re opposite nd P/ is negtive. Thus, m = = Using eqution (iii), m=-... (9.5) fe If the telescope is djusted so tht the finl imge is formed t the ner point of the eye, the ngulr mgnifiction is further incresed. Let us pply the lens eqution to the eyepiece in this cse. Here u = - EP nd v = - EP' = - D. The lens eqution is By (ii), - = v u f _ - D - EP' fe The mgnifiction is fe + D EP' f, D m = = - Length of the Telescope file + D) - fed o() (iii) = - Le ]. fe +D From figure (9.5), we see tht the length of the telescope is L = OP' P E = P' E. For norml djustment, P'E = fe so tht L = fo Ie. For djustment for ner point vision, we hve, by (iv) bove, PE- f, + D so tht the length is, L = fo + fe + D... (9.6)

6 424 Concepts of Physics (B) Terrestril Telescope In n stronomicl telescope, the finl imge is inverted with respect to the object. This cretes some prcticl difficulty if the telescope is used to see erthly objects. Imgine, how would you feel if you re viewing cricket mtch from the specttor's gllery using n stronomicl telescope. You would clerly see the turns nd breks of the bll, but the plyers would look like hnging from the field nd not stnding on the field. the - D e s derived for stronomicl telescope. Thus, (C) Glilen L= f + 4f + f e D 2f 2f Figure 9.6 To remove this difficulty, convex lens of focl length f is included between the objective nd the eyepiece in such wy tht the focl plne of the objective is distnce 2f wy from this lens (figure 9.6). The objective forms the imge P'Q' of distnt object in its focl plne. The lens L forms n imge P"Q" which is inverted with respect to P'Q'. The eyepiece is djusted in pproprite position to give the mgnified view of P"Q". The role of the intermedite lens L is only to invert the imge. The mgnifiction produced by it is, therefore, -. The mgnifying power of terrestril telescope is, therefore, obtined from (9.5) for norml djustment nd from (9.6) for ner point vision by multiplying by - on the right hnd side. Thus, for norml djustment, _ fe m nd for finl imge t ner point, T;... (9.7) m= fi) (9.8) fe [ To hve n inverted imge of sme size, the object should be plced t distnce of 2f from convex lens of focl length f. Thus, P'P" = 4f in figure (9.6) so tht the length of terrestril telescope is f + 4f + ue. For norml djustment, ue equls fe so tht the length is L = 0 + 4f + L. If the finl imge is formed t the ner point, Figure 9.7 Figure (9.7) shows simple model of Glilen telescope. A convergent lens is used s the objective nd divergent lens s the eyepiece. The objective L would form rel inverted imge P'Q' of distinct object in its focl plne. The eyepiece intercepts the converging rys in between. P'Q' then cts s virtul object for the eyepiece. The position of the eyepiece is so djusted tht the finl imge is formed t the desired position. For norml djustment, the finl imge is formed t infinity producing lest strin on the eyes. If the finl imge is formed t the lest distnce of cler vision, the ngulr mgnifiction is mximum. Mgnifying Power Suppose the objective nd the eyepiece hve focl lengths fo nd fe respectively nd the object is situted t lrge distnce uo from the objective. The object PQ subtends n ngle on the objective. Since the object is fr wy, the ngle it would subtend\ on n unided eye is lso essentilly. As uo is very lrge, the first imge PQ' is formed in the focl plne of the objective. Thus, from figure (9.8), tn ' I = P'Q' P'Q' (i) OP' L The finl imge P"Q" subtends n ngle p on the eyepiece. If the eye is plced close to the eyepiece, this is lso the ngle formed by the finl imge on the eye. From the figure, 3=3'- tn P'Q' - Ep,

7 Opticl Instruments 425 (ii) As p nd re formed on the sme side of the xis, 3 nd hve sme sign. Thus, The ngulr mgnifiction is, therefore, m p_ f. Ep fo PE (iii) 9.6 RESOLVING POWER OF A MICROSCOPE AND A TELESCOPE The resolving power of microscope is defined s the reciprocl of the distnce between two objects which cn be just resolved when seen through the microscope. It depends on the wvelength A, of the light, the refrctive index IA of the medium between the object nd the objective of the microscope, nd the ngle 0 subtended by rdius of the objective on one of the objects. It is given by 2p sine R= If the telescope is set for norml djustment, the finl imge P"Q" is formed t infinity. Then PE= - fe nd the ngulr mgnifiction is To increse the resolving power, the objective nd the object re kept immersed in oil. This increses II fo m = - fe... (9.9) nd hence R. The resolving power of telescope is defined s Note tht the focl length fe is negtive becuse the reciprocl of the ngulr seprtion between two the eyepiece is diverging lens. Thus, m is positive s distnt objects which re just resolved when viewed expected for n erect imge. If the finl imge is through telescope. It is given by formed t the ner point, the mgnifiction is - incresed. R - AO.22 X The lens formul is where is the dimeter of the objective of the = telescope. Tht is why, the telescopes with lrger u f objective perture ( m ur more) re used in For the eyepiece, stronomicl studies. v = - PE= - D, u= PE 9.7 DEFECTS OF VISION nd f= fe ve is itself negtive). As described erlier, the ciliry muscles control the Thus, curvture of the lens in the eye nd hence cn lter. the-- effective focl length of the system. When the - D fe muscles re fully relxed, the focl length is mximum. = When the muscles re strined, the curvture of the P'E lens increses nd the focl length decreses. For fe(+ Del cler vision, the imge must be formed on the retin. (iv) The imge-distnce is, therefore, fixed for cler vision nd it equls the distnce of the retin from the eyelens. It is bout 2.5 cm for grown-up person. If we By (iii), the ngulr mgnifiction is m= - [ +--- pply the lens formul to eye, the mgnitudes of the object-distnce, the imge- distnce nd the effective focl length stisfy Length of the Telescope The length of Glilen telescope is L= OE= OP' - PE = fo PE. For norml djustment, PE= - fe nd hence the length of the tube is L = fo+ fe = I fe I - For the djustment for ner point vision, by (iv), P'E= nd L - fe + D + f, D+ f, = f. I fe ID D f. I vo uo f uo - f vo Here vo is fixed, hence by chnging f, the eye cn be focused on objects plced t different vlues of uo. We see from (i) tht s f increses, uo increses nd s f decresed, uo decreses. The mximum distnce one cn see is given by () Umx fmx Vo (i)

8 426 Concepts of Physics where fm is the mximum focl length possible for the eye-lens. The focl length is mximum when the ciliry muscles re fully relxed. In norml eye, this focl length equls the distnce vo from the lens to the retin. Thus, vo = /mx, by (ii), umx = 00. A person cn theoreticlly hve cler vision of objects situted t ny lrge distnce from the eye. For the closer objects, u is smller nd hence f should be smller. The smllest distnce t which person cn clerly see, is relted to the minimum possible focl length f. The ciliry muscles re most strined in this position. By (ii), the closest distnce for cler vision is given by (iii) () Umin /min For n verge grown-up person, umm should be round 25 cm or less. This is convenient distnce t which one cn hold n object in his/her hnd nd see. Thus, norml eye cn clerly see objects plced in the rnge strting from bout 25 cm from the eye to lrge distnce, sy, of the order of severl kilometers. The nerest point where n eye cn clerly see is clled the ner point nd the frthest point upto which n eye cn clerly see is clled the fr point. For norml eye, the distnce of the ner point should be round 25 cm or less nd the fr point should be t infinity. We now describe some common decfects of vision. (A) Nersightedness A person suffering from this defect cnnot see distnt objects clerly_ This is becuse finx is less thn the distnce from the lens to the retin nd the prllel rys coming from the distnt object focus short of the retin. The ciliry muscles re fully relxed in this cse nd ny strin in it cn only further decrese the focl length which is of no help to see distnt objects. x Retin (c) Vo Figure 9.8 (b) Retin Nersightedness is lso clled Myopi. 'This my result becuse the lens is too thick or the dimeter of the eyebll is lrger thn usul. The remedy of myopi is quite simple. The rys should be mde bit divergent before entering the eye so tht they my focus little lter. Thus, divergent lens should be given to myopic person to enble him/her to see distnt objects clerly. Power of the Lens Needed Suppose, person cn see n object t mximum distnce x. Thus, with fully relxed muscles, rys coming from the distnce x converge on the retin. Figure (9.8) shows the sitution. As is cler from the figure, if the eye is to see distnt object clerly, the diverging lens should form the virtul imge of this distnt object t distnce x. Thus, the required focl length of the diverging lens is f = - x nd the power is Exmple 9.3 f - x A nersighted mn cn clerly see objects up to distnce of '5 m. Clculte the power of the lens of the spectcles necessry for the remedy of this defect. Solution : The lens should form virtul imge of distnt object t '5 m from the lens. Thus, it should be divergent lens nd its focl length should be -.5 m. Hence, (B) Frsightedness f=-.5m P=7=-T-5-m 0.67D. Retin A person suffering from frsightedness cnnot clerly see objects close to the eye. The lest distnce for cler vision is pprecibly lrger thn 25 cm nd the person hs to keep the object inconveniently wy from the eye. Thus, reding newspper or viewing smll thing held in the hnds is difficult for such person. Frsightedness is lso known s hyperopi. Generlly, it occurs when the eye-lens is too thin t the centre nd/or the eyebll is shorter thn norml. The ciliry muscles even in their most strined position re not ble to reduce the focl length to pproprite vlue. The defect cn lso rise if the ciliry muscles become wek nd re not ble to strin enough to reduce the focl length to pproprite vlue. When frsightedness develops due to this reson, it is known s presbyopi.

9 Opticl Instruments 427 () I 25cm ---I (c) Figure 9.9 Figure (9.9) shows the sitution nd the remedy for frsightedness. The rys strting from the norml ner point 25 cm would focus behind the retin. They should be mde bit less divergent before sending them to the eye so tht they my focus on the retin. This cn be chieved by putting converging lens in front of the eye. Suppose, the eye cn clerly see n object t minimum distnce y. If the eye is to see clerly n object t 25 cm, the converging lens should form n imge of this object t distnce y (figure 9.9c). Here u = - 25 cm nd v = - y. Using the lens formul - v u f, we get -y - 25 cm f P = 25 cm y (C) Astigmtism Another kind of defect rises in the eye when the eye-lens develops different curvtures long different (b) plnes. Such person cnnot see ll the directions eqully well. A prticulr direction in the plne perpendiculr to the line of sight is most visible. The direction perpendiculr to this is lest visible. Here is `do it yourself ' test for stigmtism. Figure (9.0) shows four lines pssing through point. The lines re ssumed to be drwn with equl intensity (you cn drw such lines on pper with equl intensity nd do the test). If you cn see ll the lines eqully distinct nd intense, you re not stigmtic. If prticulr line sy (2)-(2) ppers to be most intense nd the perpendiculr line (4)-(4) ppers lest intense, you re most likely stigmtic. If it is so, rotte the book through right ngle so tht (2)-(2) tkes the plce of (4)-(4) nd vice vers. If you re relly stigmtic, you will find tht now (4)-(4) ppers most intense nd (2)-(2) ppers lest intense. 2 Figure 9.0 The remedy to stigmtism is lso pinless. Glsses with different curvtures in different plnes re used to compenste for the deshping of the eyelens. Opticins cll them cylindricl glsses. A person my develop ny of the bove defects or combintion of more thn one. Quite common in old ge is the combintion of nersightedness nd frsightedness. Such person my need converging glss for reding purpose nd diverging glss for seeing t distnce. Such persons either keep two sets of spectcles or- spectcle with upper portion divergent nd lower portion convergent (bifocl). 2. An object is seen through simple microscope of focl length 2 cm. Find the ngulr mgnifiction produced if the imge is formed t the ner point of the eye which is 25 cm wy from it. Solution : The ngulr mgnifiction produced by simple microscope when the imge is formed t the ner point of the eye is given by m + 7. Here f =. 2 cm, D = 25 cm. Hence, Worked Out. Exmples m = + 2 = 3' A 0 D lens is used s mgnifier. Where should the object be plced to obtin mximum ngulr mgnifiction for norml eye (ner point = 25 cm)? Solution : Mximum ngulr mgnifiction is chieved when the finl imge is formed t the ner point. Thus, v = - 25 cm. The focl length is f = m - 0 cm.

10 428 Concepts of Physics We hve, _ = u 7 25 cm u 0 cm _ u 25 cm 0 cm 50 cm = - 7. cm A smll object is plced t distnce of 3.6 cm from mgnifier of focl length 4.0 cm. () Find the position of the imge. (b) Find the liner mgnifiction. (c) Find the ngulr mgnifiction. Solution : () Using + u f - 3'6 cm 4.0 cm v = - 36 cm. (b) Liner mgnifiction = - 36 cm = cm ' (c) If the object is plced t distnce uo from the lens, the ngle subtended by the object on the lens is 3 = where h is the height of the object. The mximum ngle subtended on the unided eye is = Thus, the ngulr mgnifiction is D 25 cm uo 3'6 cm = A compound microscope consists of n objective of focl length '0 cm nd n eyepiece of focl length 5.0 cm seprted by 2'2 cm. () At wht distnce from the objective should n object be plced to focus it properly so tht the finl imge is formed t the lest distnce of cler vision (25 cm)? (b) Clculte the ngulr mgnifiction in this cse. Solution : () For the eyepiece, ve - 25 cm nd cm. Using _ ve /Le fe ue ye fe = - 25 cm 5 cm Lie cm - - 4'7 cm = cm. Figure 9-W As the objective is 2'2 cm wy from the eyepiece, the imge formed by the objective is 2'2 cm - 4'2 cm = 8.0 cm wy from it. For the objective, Using cm, fo = + '0 cm. - u= fo' u - 8'0 cm PO cm u = - 80 cm = - ' cm. (b) The ngulr mgnifiction is m = { + /2) u fe cm _ + 25 cm) = cm 5 cm 5. The seprtion L between the objective (f = 0.5 cm) nd the eyepiece (f = 5 cm) of compound microscope is 7 cm. Where should smll object be plced so tht the eye is lest strined to see the imge? Find the ngulr mgnifiction produced by the microscope. Solution : The eye is lest strined if the finl imge is formed t infinity. In such cse, the imge formed by the objective should fll t the focus of the eyepiece. As 4-5 cm nd L = 7 cm, this first imge should be formed t 7 cm - 5 cm = 2 cm from the objective. Thus, o = + 2 cm. Also, f, = 0.5 cm. For the objective, using _ u fo _ u v f,, 2 cm 0'5 cm

11 2 / = -3 cm. Figure 9-W2 The ngulr mgnifiction in this cse is v D m = u 2 cm 25 cm - (2/3) cm 5 cm - 5' 6. An stronomicl telescope hs n objective of focl length 200 cm nd' n eyepiece of focl length 4.0 cm. The telescope is focused to see n object 0 km from the objective. The finl imge is formed t infinity. Find the length of the tube nd the ngulr mgnifiction produced by the telescope. Solution : As the object distnce 0 km is much lrger thn the focl length 200 cm, the first imge is formed lmost t the focus of the objective. It is thus 200 cm from the objective. This imge cts s the object for the eyepiece. To get the finl imge t infinity, this first imge should be t the first focus of the eyepiece. The length of the tube is, therefore, 200 cm + 4 cm = 204 cm. The ngulr mgnifiction in this cse fo 200 m = - = - 4 = fe 7. A Glilen telescope is constructed by n objective of focl length 50 cm nd n eyepiece of focl length 5.0 cm. () Find the tube length nd mgnifying power when it is used to see n object t lrge distnce in norml djustment. (b) If the telescope is to focus n object 2.0 m wy from the objective, wht should be the tube length nd ngulr mgnifiction, the imge gin forming t infinity? Solution : () nd f, = 50 cm, fe - 5 cm. L= fo fe I = (50-5) cm = 45 cm fo m=- 50 = 0. (b) Using the eqution - - for the objective, v u f Opticl Instruments 429 The tube length v fo u 50 cm cm v = cm. L v - I fe I. (66'67-5) cm L = 6'67 cm. To clculte the ngulr mgnifiction, we ssume tht the object remins t lrge distnce from the eye. In this cse, the ngulr mgnifiction v m = = '33. fe 5 v is the distnce of the first imge from the objective which is substituted for [0. 8. The imge of the moon is focused by converging lens of focl length 50 cm on plne screen. The imge is seen by n unided eye from distnce of 25 cm. Find the ngulr mgnifiction chieved due to the converging. lens. Solution : Figure 9-W3 Suppose the moon subtends n ngle on the lens. This will lso be the ngle subtended by the moon on the eye if the moon is directly viewed. The imge is formed in the focl plne. The liner size of the imge f = (50 cm). If this imge is seen from distnce of 25 cm, the ngle formed by the imge on the eye (50 cm)] P I cm The ngulr mgnifiction is 9. The ner nd fr points of person re t 40 cm nd 250 cm respectively. Find the power of the lens he/she should use while reding t 25 cm. With this lens on the eye, wht mximum distnce is clerly visible?

12 430 Concepts of Physics Solution : If n object- is plced t 25 cm from the correcting lens, it should produce the virtul imge t 40 cm. Thus, u = - 25 cm, u = - 40 cm. f u u 40 cm 25 cm f=-t-cm=+-5-m P = f.5 D. The unided eye cn see mximum distnce of 250 cm. Suppose the mximum distnce for cler vision is d when the lens is used. Then the object t distnce d is imged by the lens t 250 cm. We hve, u f cm d 200 cm d= -53 cm. Thus, the person will be ble to see upto mximum distnce of 53 cm.. Cn virtul imge be formed on the retin in seeing process? 2. Cn the imge formed by simple microscope be projected on screen without using ny dditionl lens or mirror? 3. The ngulr mgnifiction of system is less thn one. Does it men tht the imge formed is inverted? 4. A simple microscope using single lens often shows coloured imge of white source. Why? 5. A mgnifying glss is converging lens plced close to the eye. A frsighted person uses spectcles hving converging lenses. Compre the functions of converging lens used s mgnifying glss nd s spectcles. 6. A person is viewing n extended object. If converging lens is plced in front of his eyes, will he feel tht the size hs incresed? 7. The mgnifying power of converging lens used s simple microscope is { + D. A compound microscope is f combintion of two such converging lenses. Why don't we hve mgnifying power 0 0. A young boy cn djust the power of his eye-lens between 50 D nd 60 D. His fr point is infinity. () Wht is the distnce of his retin from the eye-lens? (b) Wht is his ner point? Solution : () When the eye is fully relxed, its focl length is lrgest nd the power of the eye-lens is minimum. This power is 50 D ccording to the given dt. The focl length is m = 2 cm. As the fr point is t infinity, the 5 0 prllel rys coming from infinity re focused on the retin in the fully relxed condition. Hence, the distnce of the retin from the lens equls the focl length which is 2 cm. (b) When the eye is focused t the ner point, the power is mximum which is 60 D. The focl length in this cse is f = m- 5 cm. The imge is formed on the retin 60 3 nd thus u = 2 cm. We hve, - u f 3 u = u f 2 cm 5 cm u = - 0 cm. The ner point is t 0 cm. QUESTIONS FOR SHORT ANSWER [ + 2 / ill + 2., ]? In other lo le words, why cn the objective not be treted s simple microscope but the eyepiece cn? 8. By mistke, n eye surgeon puts concve lens in plce of the lens in the eye fter ctrct opertion. Will the ptient be ble to see clerly ny object plced t ny distnce? 9. The mgnifying power of simple microscope is given by + where D is the lest distnce for cler vision. For frsighted persons, D is greter thn the usul. Does it men tht the mgnifying power of simple microscope is greter for frsighted person s compred to norml person? Does it men_ tht frsighted person cn see n insect more clerly under microscope thn norml person? 0. Why re the mgnifiction properties of microscopes nd telescopes defined in terms of the rtio of ngles nd not in terms of the rtio of sizes of objects nd imges?. An object is plced t distnce of 30 cm from converging lens of focl length 5 cm. A norml eye (ner point 25 cm, fr point infinity) is plced close to the lens on the other side. () Cn the eye see the object clerly? (b) Wht should be the minimum seprtion between the lens nd the eye so tht the eye cn clerly see the

13 Opticl Instruments 43 object? (c) Cn diverging lens, plced in contct with the converging lens, help in seeing the object clerly when the eye is close to the lens? 2. A compound microscope forms n inverted i'rnge of n object. In which of the following cses it is likely to crete difficulties? () Looking t smll germs. (b) Looking t circulr spots. (c) Looking t verticl tube contining some wter. OBJECTIVE I. The size of n object s perceived by n eye depends primrily on () ctul size of the object (b) distnce of the object from the eye (c) perture of the pupil (d) size of the imge formed on the retin. 2. The muscles of norml eye re lest strined when the eye is focused on n object () fr wy from the eye (b) very close to the eye (c) t bout 25 cm from the eye (d) t bout m from the eye. 3. A norml eye is not ble to see objects closer thn 25 cm becuse () the focl length of the eye is 25 cm (b) the distnce, of the retin from the eye-lens is 25 cm (c) the eye is not ble to decrese the distnce between the eye-lens nd the retin beyond limit (d) the eye is not ble to decrese the focl length beyond limit. 4. When objects t different distnces re seen by the eye, which of the following remin constnt? () The focl length of the eye-lens. (b) The object-distnce from the eye-lens. (c) The rdii of curvture of the eye-lens. (d) The imge-distnce from the eye-lens. 5. A person A cn clerly see objects between 25 cm nd 200 cm. Which of the following my represent the rnge of cler vision for person B hving muscles stronger OBJECTIVE II thn A, but ll other prmeters of eye identicl to tht of A? () 25 cm to 200 cm (b) 8 cm to 200 cm (c) 25 cm to 300 cm (d) 8 cm to 300 cm. 6. The focl length of norml eye-lens is bout () mm (b) 2 cm (c) 25 cm (d) m. 7. The distnce of the eye-lens from the retin is x. For norml eye, the mximum focl length of the eye-lens () = x (b) < x (c) > x (d) = 2 x. 8. A mn wering glsses of focl length + m cnnot clerly see beyond m () if he is frsighted (b) if he is nersighted (c) if his vision is norml (d) in ech of these cses. 9. An object is plced t distnce u from simple microscope of focl length f. The ngulr mgnifiction obtined depends () on f but not on u (b) on u but not on f (c) on f s well s u (d) neither on f nor on u. 0. To increse the ngulr mgnifiction of simple microscope, one should increse () the focl length of the lens (b) the power of the lens (c) the perture of the lens (d) the object size.. A mn is looking t smll object plced t his ner point. Without ltering the position of his eye or the object, he puts simple microscope of mgnifying power 5 X before his eyes. The ngulr mgnifiction chieved is () 5 (b) 2'5 (c) (d) 0'2.. When we see n object, the imge formed on the retin is () rel (b) virtul (c) erect (d) inverted. 2. In which of the following the finl imge is erect? () Simple microscope. (b) Compound microscope. (c) Astronomicl telescope. (d) Glilen telescope. 3. The mximum focl length of the eye-lens of person is greter thn its distnce from the retin. The eye is () lwys strined in looking t n object (b) strined for objects t lrge distnces only (c) strined for objects t short distnces only (d) unstrined for ll distnces. 4. Mrk the correct options. () If the fr point goes hed, the power of the divergent lens should be reduced. (b) If the ner point goes hed, the power of the convergent lens should be reduced. (c) If the fr point is m wy from the eye, divergent lens should be used. (d) If the ner point is m wy from the eye, divergent lens should be used. 5. The focl length of the objective of compound microscope is 0 nd its distnce from the eyepiece is L. The object is plced t distnce u from the objective. For proper working of the instrument, () L < u (b) L > u (c) fo < L < 2f0 (d) L > 2fo.

14 432 Concepts of Physics. A person looks t different trees in n open spce with the following detils. Arrnge the trees in decresing order of their pprent sizes. BSI Height(m) Distnce from the eve(m_i A B C.8 70 D An object is to be seen through simple microscope of focl length 2 cm. Where should the object be plced so s to produce mximum ngulr mgnifiction? The lest distnce for cler vision is 25 cm. 3. A simple microscope hs mgnifying power of 3'0 when the imge is formed t the ner point (25 cm) of norml eye. () Wht is its focl length? (b) Wht will be its mgnifying power if the imge is formed t infinity? 4. A child hs ner point t 0 cm. Wht is the mximum ngulr mgnifiction the child cn hve with convex lens of focl length 0 cm? 5. A simple microscope is rted 5 X for norml relxed eye. Wht will be its mgnifying power for relxed frsighted eye whose ner point is 40 cm? 6. Find the mximum mgnifying power of compound Microscope hving 25 diopter lens s the objective, 5 diopter lens s the eyepiece nd the seprtion 30 cm between the two lenses. The lest distnce for cler vision is 25 cm. 7. The seprtion between the objective nd the eyepiece of compound microscope cn be djusted between 9.8 cm to '8 cm. If the focl lengths of the objective nd the eyepiece re '0 cm nd 6 cm respectively, find the rnge of the mgnifying power if the imge is lwys needed t 24 cm from the eye. 8. An eye cn distinguish between two points of n object if they re seprted by more thn 0.22 mm when the object is plced t 25 cm from the eye. The object is now seen by compound microscope hving 20 D objective nd 0 D eyepiece seprted by distnce of 20 cm. The finl imge is formed t 25 cm from the eye. Wht is the minimum seprtion between two points of the object which cn now be distinguished? 9. A compound microscope hs mgnifying power of 00 when the imge is formed t infinity. The objective hs focl length of 0.5 cm nd the tube length is 6.5 cm. Find the focl length of the eyepiece. 0. A compound microscope consists of n objective of focl length cm nd n eyepiece of focl length 5 cm. An object is plced t distnce of 0.5 cm from the objective. Wht should be the seprtion between the lenses so tht the microscope projects n inverted rel imge of the object on screen 30 cm behind the eyepiece?. An opticl instrument used for ngulr mgnifiction hs 25 D objective nd 20 D eyepiece. The tube length is 25 cm when the eye is lest strined. EXERCISES () Whether it is microscope or telescope? (b) Wht is the ngulr mgnifiction produced? 2. An stronomicl telescope is to be designed to hve mgnifying power of 50 in norml djustment. If the length of the tube is 02 cm, find the powers of the objective nd the eyepiece. 3. The eyepiece of n stronomicl telescope hs focl length of 0 cm. The telescope is focused for norml vision of distnt objects when the tube length is.0 m. Find the focl length of the objective nd the mgnifying power of the telescope. 4. A Glilen telescope is 27 cm long when focused to form n imge t infinity. If the objective hs focl length of 30 cm, wht is the focl length of the eyepiece? 5. A frsighted person cnnot see objects plced closer to 50 cm. Find the power of the lens needed to see the objects t 20 cm. 6. A nersighted person cnnot clerly see beyond 200 cm. Find the power of the lens needed to see objects t lrge distnces. 7. A person wers glsses of power D. Is the person frsighted or nersighted? Wht is the fr point of the person without the glsses? 8. A professor reds greeting crd received on his 50th birthdy with D glsses keeping the crd 25 cm wy. Ten yers lter, he reds his frewell letter with the sme glsses but he hs 'to keep the letter 50 cm wy. Wht power of lens should he now use? 9. A norml eye hs retin 2 cm behind the eye-lens. Wht is the power of the eye-lens when the eye is () fully relxed, (b) most strined? 20. The ner point nd the fr point of child re t 0 cm nd 00 cm. If the retin is 2.0 cm behind the eye4ens, wht is the rnge of the power of the eye-lens? 2. A nersighted person cnnot see beyond 25 cm. Assuming tht the seprtion of the glss from the eye is cm, find the power of lens needed to see distnt objects. 22. A person hs ner point t 00 cm. Wht power of lens is needed to red t 20 cm if he/she uses () contct lens, (b) spectcles hving glsses 2'0 cm seprted from the eyes? 23. A ldy uses + '5 D glsses to hve norml vision from 25 cm onwrds. She uses 20 D lens s simple microscope to see n object. Find the mximum mgnifying power if she uses the microscope () together with her glss (b) without the glss. Do the nswers suggest tht n object cn be more clerly seen through microscope without using the correcting glsses? 24. A ldy cnnot see objects closer thn 40 cm from the left eye nd/closer thn 00 cm from the right eye. While on mountineering' trip, she is lost from her tem. She tries to mke n stronomicl telscope/ from her reding glsses to look for her temmtes. () Which glss should she use s the eyepiece? (b) Wht mgnifiction cn she get with relxed eye?

15 Downloded from Opticl Instruments 433 ANSWERS OBJECTIVE I to '04 mm. (d) 2. () 3. (d) 4. (d) 5. (b) 6. (b) 9. 2 cm 7. () 8. (d) 9. (c) 0. (b). (c) 0. 5 cm. microscope, 20 OBJECTIVE II 2. D, 50 D cm, 9. (), (d) 2. (), (d) 3. () 4. 3 cm 4. (), (c) 5. (b), (d) 5. 3 D D EXERCISES 7. nersighted, 40 cm '5 D. A, B, D, C D, 54 D cm from the lens D to + 5 D 3. () 2'5 cm (b) D D, + 4'53 D 5. 8 X 23. 6, right lens, 2 0