SOLUTIONS TO CONCEPTS CHAPTER 9. Th isal angls mad by th tr with th ys can b calclatd b blow. Hight o th tr AB 2 = A.4 Distanc rom th y OB 5 similarly, B = 2.5 / 8 =.25 C =.8 / 7 =.257 D = 2.8 / =.28 Sinc, A > B > D > C, th arrangmnt in dcrasing ordr is gin by A, B, D and C. 2. For th gin simpl microscop, = 2 cm and D = 25 cm For maximm anglar magniication, th imag shold b prodcd at last distanc o clar ision. = D = 25 cm 7 25 2 = 8. cm th objct shold b placd 8. cm away rom th lns.. Th simpl microscop has, m =, whn imag is ormd at D = 25 cm a) m = D 25 = 25/2 = 2.5 cm b) Whn th imag is ormd at ininity (normal adjstmnt) Magniying powr = D 25 = 2. 2.5 4. Th child has D = cm and = cm Th maximm anglar magniication is obtaind whn th imag is ormd at nar point. D m = = + = 2 5. Th simpl microscop has magniication o 5 or normal rlaxd y (D = 25 cm). Bcas, th y is rlaxd th imag is ormd at ininity (normal adjstmnt) m = 5 = D 25 = 5 cm For th rlaxd arsightd y, D = 4 cm m = D 4 = 8 5 its magniying powr is 8X. Distanc A B A B D=25cm A B (Simpl Microscop) + hight 9.
6. For th gin compond microscop = 25 dioptr =.4 m = 4 cm, = 5 dioptr =.2 m = 2 cm D = 25 cm, sparation btwn objcti and ypic = cm Th magniying powr is maximm whn th imag is ormd by th y pic at last distanc o clar ision i.. D = 25 cm or th y pic, = 25 cm, = 2 cm For lns ormla, 25 2 =. cm or th objcti lns, th imag distanc shold b = (.) = 8.89 cm or th objcti lns, = +8.89 cm (bcas ral imag is prodcd) = 4 cm =.5.25 =.97 8.89 4 o o o o = 5.7 cm th maximm magniicnt powr is gin by o D 8.89 25 m = o 5.7 2 =.7225 2.25 = 8.76 7. For th gin compond microscop o = cm, = 6 cm, D = 24 cm For th y pic, = 24 cm, = 6 cm 5 24 6 24 9.2 Chaptr 9 = 4.8 cm a) Whn th sparation btwn objcti and y pic is 9.8 cm, th imag distanc or th objcti lns mst b (9.8) (4.8) = 5. cm = 4 = = = 5 5 = 4 5 =.25 cm th magniying powr is gin by, D 5 m = = 24 = 4 5 = 2.25 6 o (b) Whn th sparation is.8 cm, =.8 4.8 = 7. cm, = cm = 6 = = 7 7 A B o =.4m objcti A B A cm B 25cm =.2m objcti. cm 5 cm 9.8cm 24 cm Fig-A 7 cm Fig-B 4.8cm 4.8cm.8cm 24 cm
D 7 m = = o 24 = 6 5 = 7 6 6 th rang o magniying powr will b 2 to. 8. For th gin compond microscop. = 2D =.5 m = 5 cm, = D =. m = cm. 9. Chaptr 9 D = 25 cm, sparation btwn objcti & ypic= 2 cm For th minimm sparation btwn two points which can b distingishd by y sing th microscop, th magniying powr shold b maximm. For th ypic, = 25 cm, = cm 2 5 = = = 25 5 5 = cm 7 th imag distanc or th objcti lns shold b, 5 9 V = 2 = cm 7 7 or th objcti lns, = 7 = 9 5 9 9 = cm th maximm magniying powr is gin by, m = D 9 = 7 25 9 =. 5 = 5.5 7.22 Ths, minimm sparation y can distingish = mm =.4 mm 5.5 9. For th gi compond microscop, =.5cm, tb lngth = 6.5cm magniying powr = (normal adjstmnt) Sinc, th imag is ormd at ininity, th ral imag prodcd by th objcti lns shold li on th ocs o th y pic. + = 6.5 cm () Again, magniying powr= D m = 25 =.5 = ( 2 ) 25 2 4 = (2) D [or normal adjstmnt] [Taking D = 25 cm] Objcti F Ey pic
Soling qation () and (2) w can gt, V = 4.5 cm and = 2 cm th ocal lngth o th y pic is 2cm.. Gin that, o = = cm, = 5 cm, =.5 cm, = cm For th objcti lns, =.5 cm, = cm. From lns ormla, = =.5 Chaptr 9 = cm 6cm a irtal imag is ormd by th objcti on th sam sid as that o th objct at a distanc o cm rom th objcti lns. This imag acts as a irtal objct or th ypic. For th ypic, = 5 = 5 as shown in igr, Sparation btwn th lnss = = 6 = 5 cm. Th optical instrmnt has = 25D =.4 m = 4 cm = 6 = 6 cm = =.5 m = 5 cm 2D tb lngth = 25 cm (normal adjstmnt) (a) Th instrmnt mst b a microscop as < (b) Sinc th inal imag is ormd at ininity, th imag prodcd by th objcti shold li on th ocal plan o th y pic. imag distanc or objcti = = 25 5 = 2 cm sing lns ormla. = 4 = 2 4 2 = 5 D anglar magniication = m = [Taking D = 25 cm] 2 5 25 5 = 5 cm = = 2 2. For th astronomical tlscop in normal adjstmnt. Magniying powr = m = 5, lngth o th tb = L = 2 cm Lt and b th ocal lngth o objcti and y pic rspctily. m = = 5 = 5 () and, L = + = 2 cm (2) Ptting th al o rom qation () in (2), w gt, + = 2 5 = 2 = 2 cm =.2 m = cm = m A B cm A B A B.5cm Objcti Objcti 2cm F F Ey pic 5cm cm B A Ey pic Powr o th objcti lns = And Powr o th y pic lns = = D =. 2 = 5D 9.4
Chaptr 9. For th gin astronomical tlscop in normal adjstmnt, F = cm, L = m = cm S, = L = = 9 cm and, magniying powr = 9 = = 9 4. For th gin Galilan tlscop, (Whn th imag is ormd at ininity) = cm, L = 27 cm Sinc L = [Sinc, conca ypic lns is sd in Galilan Tlscop] = L = 27 = cm 5. For th ar sightd prson, = 2 cm, = 5 cm rom lns ormla = = 5 2 = 2 5 powr o th lns = = Dioptr 6. For th nar sightd prson, = and = 2 cm = 2m 2 = = =.5 2 powr o th lns is.5d 7. Th prson wars glasss o powr 2.5D th prson mst b nar sightd. =, = ar point, = = 4 2.5 = 4 cm = =.4m = 4 cm cm = m th ar point o th prson is 4 cm 8. On th 5 th birthday, h rads th card at a distanc 25cm sing a glass o +2.5D. Tn yars latr, his nar point mst ha changd. So atr tn yars, = 5 cm, = 2.5D = =.4m = 4 cm = nar point 5 4 nar point = = 2cm To rad th arwll lttr at a distanc o 25 cm, U = 25 cm For lns ormla, = = 2 25 Powr o th lns = = 2 9 = 4.5D = 2 9 = 2 25 2 = 2 2 cm = m 9 9 H has to s a lns o powr +4.5D. 9.5
9. Sinc, th rtina is 2 cm bhind th y-lns = 2cm (a) Whn th y-lns is lly rlaxd =, = 2cm =.2 m = = 5D.2 in this condition powr o th y-lns is 5D (b) Whn th y-lns is most straind, = 25 cm =.25 m, = +2 cm = +.2 m = = 5 + 4 = 54D.2.25 In this condition powr o th y lns is 54D. 2. Th child has nar point and ar point cm and cm rspctily. Sinc, th rtina is 2 cm bhind th y-lns, = 2cm For nar point = cm =. m, = 2 cm =.2 m nar =.2 For ar point, = cm = m, ar =.2 = 5 + = 6D. = 5 + = 5D = 2 cm =.2 m th rag o powr o th y-lns is +6D to +5D 2. For th nar sightd prson, = distanc o imag rom glass = distanc o imag rom y sparation btwn glass and y = 25 cm cm = 24 cm =.24m or th glass, = and = 24 cm =.24m =.24 = 4.2 D 22. Th prson has nar point cm. It is ndd to rad at a distanc o 2cm. (a) Whn contact lns is sd, = 2 cm =.2m, = cm = m =.2 (b) Whn spctacls ar sd, = (2 2) = 8 cm =.8m, =.8 = + 5 = + 4D = cm = m = + 5.55 = + 4.5D 2. Th lady ss +.5D glasss to ha normal ision at 25 cm. with th glasss, hr last distanc o clar ision = D = 25 cm Focal lngth o th glasss = m = cm.5. 5 withot th glasss hr last distanc o distinct ision shold b mor Ey lns 2cm Chaptr 9 Rtina I, = 25cm, = =.5 cm.5.5 4 = 25 2. 5 = = 4cm = nar point withot glasss. Focal lngth o magniying glass = 2 m =.5m = 5 cm = 9.6
(a) Th maximm magniying powr with glasss D 25 m = = = 6 [D = 25cm] 5 (b) Withot th glasss, D = 4cm D 4 m = = = 9 5 24. Th lady can not s objcts closr than 4 cm rom th lt y and cm rom th right y. For th lt glass lns, = 4 cm, = 25 cm = 4 25 For th right glass lns, = cm, = 25 cm = = 25 4 2 = 2 cm Chaptr 9 = = = = cm 25 25 (a) For an astronomical tlscop, th y pic lns shold ha smallr ocal lngth. sh shold s th right lns ( = cm) as th y pic lns. (b) With rlaxd y, (normal adjstmnt) = 2 cm, = magniication = m = cm = 2 / / = 2 9.7