INDIAN ASSOCIATION OF PHYSICS TEACHERS NATIONAL STANDARD EXAMINATION IN PHYSICS

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1 INDIAN ASSOCIATION OF HYSICS TEACHES NATIONAL STANDAD EXAMINATION IN HYSICS 00-0 Tal ie : 0 inues (A-, A- & ) AT - A (Tal Marks : 80) SU-AT A- Q. Displaceen f an scillaing paricle is gien by y = A sin (x + C + D). The diensinal frula fr [ACD] is - (A) [M 0 L T 0 ] () [M 0 L 0 T ] (C) [M 0 L T ] (D) [M 0 L 0 T 0 ] Apply he rules f diensinal analysis. The quaniy A us hae he diensins f displaceen. The brackeed quaniy us be diensinless and hence, us hae he diensins f reciprcal f displaceen, C us hae he diensins f reciprcal f ie and D us be diensinless. Q. Tw sall spheres f equal asses sar ing in ppsie direcins fr a pin A in a hriznal circular rbi wih angenial elciies and respeciely. eween cllisins, he spheres e wih cnsan speeds. The nuber f elasic cllisins he spheres will ake befre hey reach pin A again is - (A) 4 () (C) (D) [C] efer he figure. The firs cllisin will ake place a pin. Due elasic cllisin, he spheres will exchange heir elciies and cllide a pin C, again here will be an exchange f elciies and he bdies will ce pin A cllide fr he nex ie. A spring balance and disance f hk fr he hinge pin f he inclined plane. The graph ha crrecly represens his ariain is : (A) (C) f f d 4 5 () (D) Spring balance d d [A] The reading n he spring balance is he frce required lif he plane. Since he angular displaceen is he sae eery ie, he wrk dne is fixed and hence he rque. In her wrds he prduc f frce and disance f pin f applicain f frce fr he hinge us be cnsan. f f d Q. On ne ar f an inclined plane 5 hks are fixed (a he sae separain) lif he upper ar relaie he her ar kep hriznal as shwn. The hk fixed n he inclined plane is lifed hrugh he sae angle wih he help f a spring balance, using hk,,, 4, 5 in rder. A graph is pled beween he reading f C Q.4 Idenical pin asses are placed a (n ) erices f a regular plygn f n sides. The acan erex has a psiin ecr a wih respec he cenre f he plygn. Therefre, he psiin ecr f he cenre f ass f he syse is - (A) (n ) a (C) na a () (n ) a (D) n

2 Ne ha he cenre f ass will ge shifed in he ppsie direcin wih reference he psiin ecr f he acan erex Q.5 Three idenical balls ing geher alng a hriznal line wih elciy cllide wih w siilar balls a res alng he sae line. The cllisin is elasic. Afer he cllisin - (A) w balls e wih elciy. () w balls e wih elciy (C) hree balls e wih elciy (D) hree balls e wih elciy [C] As per he law f cnserain f linear enu, he w balls riginally a res alng wih ne fr hse already in in will e wih elciy. Tw f he hree balls riginally ing will naurally ce res. Q.6 A blck is placed n a surface wih erical x crss secin gien by he equain y =. If 0 he cefficien f fricin is 0.5, he axiu heigh abe he grund a which a blck can be placed wihu slipping is - (A).00 ().5 (C).50 (D).90 y drawing he usual free bdy diagra, we can wrie, in equilibriu g sin = μ s N and g cs = N giing an = μ s. u an dy x x = =. This gies 0.5 = dx 0 0 x = 5. x Use his alue in he equain y = 0 axiu heigh y =.5 ge Q.7 Le L be he lengh and d be he diaeer f crss secin f a wire. Differen lenghs f wire f he sae aerial are subjeced he sae ensin. In which f he fllwing cases will he exensin be axiu? (A) L = 00 c, d =.0 () L = 00 c, d = 0.5 (C) L = 00 c, d = 0. (D) L = 50 c, d = 0.05 [D] L L Exensin l l A. The exensin d is biusly axiu in case f pin (d). Q.8 Cnsider an expressin F = Ax sin () where F represens frce, x represens disance and represens ie. Diensinally he quaniy A represens - (A) energy () surface ensin (C) inensiy f ligh (D) pressure [C] Diensinal analysis suggess ha he quaniy Ax n HS us hae he diensins f frce whereas us hae he diensins f reciprcal f ie. Then, he prduc A will hae he diensins f energy per uni area per uni ie, he sae as hse f inensiy f ligh. Q.9 Velciy displaceen cure f a paricle ing in a sraigh line is as shwn. Line is nral he cure and line A is nral he X axis. The insananeus accelerain f he paricle a is /s (0, 4) O A(, 0) (, 0) S (A) /s ().5 /s (C) /s (D) zer [C] d Accelerain can be wrien as = an ds where (an ) is he slpe f he gien cure and her sybls hae heir usual eanings. Since he slpe f is 4. The slpe f he cure an = 4. uing hese alues, we ge he accelerain as /s. Q.0 Suppse ha he graiainal frce aries inersely as he n h pwer f he disance. Then, he perid f a plane in circular rbi f radius arund he sun will be prprinal - n n (A) () (C) n (D) n/

3 [A] In his case we can wrie, GM n = = r T 4 = T GM This gies he desired resul. n. Q. In he circui shwn, he penial differences acrss C and C are respeciely 400 C = 5 μf G 00 Q. A plane f ass es arund he sun f ass M in an ellipical rbi. The axiu and iniu disances f he plane fr he sun are r and r respeciely. Therefre, he ie perid f he plane is prprinal - (A) (r + r ) () (r + r ) / (C) (r + r ) / (D) (r + r ) 4 The sei-ajr axis f he ellipical rbi f r r plane arund he sun is. Wih he sun a he fcus, Kepler's law hen gies he prprinaliy. Q. One le f an ideal is aken fr an iniial sae A ( 0, V 0 ) a final sae ( 0, V 0 ) by w differen prcesses. () Gas expands isherally duble is lue and hen pressure is dubled a cnsan lue he final sae. () Gas is cpressed isherally unil is pressure is dubled and hen is lue is dubled a cnsan pressure he final sae. The p -V diagra ha crrecly represen he w prcesses is : (A) p 0 p 0 () p 0 p 0 A A O 0 0 V O 0 0 V p 0 p 0 (C) p 0 A (D) p 0 O 0 0 V O 0 0 V [C] Since he firs sep in bh he prcesses is isheral, we hae pv = cnsan giing he pv diagra he shape f a recangular hyperbla. This is bsered in pin (C) nly and hence he answer. C = 4 μf V (A) l, l () l,. l (C) l, l (D) l, l The al curren in he circui flws hrugh he w resisrs and he galaneer nly and i is equal A. This prduces a drp f l acrss C and a drp f. l acrss C. Q.4 A ball is drpped fr a heigh h abe a hriznal cncree surface. The cefficien f resiuin fr he cllisin inled is e. The ie afer which he ball sps buncing is - (A) h g e () h g e h e h (C) (D) g e g e [C] The ie required fr he free fall f he ball is h. Then he ie aken fr rise and nex fall g h will be (e). The ie aken fr ne re g h rise and fall will be (e ) ec. Therefre, g he al ie fr which he ball will be in in, will be h e( + e + e +.) = h g g h h h e e g g e g e This n siplificain gies he resul. Q.5 A eal blck is resing n a rugh wden surface. A hriznal frce applied he blck is increased unifrly. Which f he fllwing cures crrecly represens elciy f he blck?

4 (A) (C) () (D) [C] Le f = μ s N a =. Therefre, = 0 fr <. Fr > ne frce n he blck = k b where d b = μ k N. Therefre, = k b d = k b A. Nw, A = 0 since = 0 a = 0. Thus, graph f agains is a parablic cure as in (c). Q.6 The earh has ass M and radius. Siilarly he sun has ass M and radius. Disance beween heir cenres is r. I is knwn ha he cenre f ass f he earh-sun syse lies well wihin he sun. Therefre. M M (A) () M M r M M r (C) M < M (D) M > M Disance f cenre f ass fr cenre f he sun Mr will be. Since he cenre f ass lies M M wihin he sun resul. Mr M M < and hence he Q.7 Cnsider a paricle f a rigid bdy. Is in can be described by ecrs r,, a r,a,and (sybls hae heir usual eanings). Then, which f he fllwing equains is incrrec? d (A) () r d (C) ( r) (D) r a r a Vecr relain beween linear elciy and angular elciy is r, s ha pin (b) is incrrec. Q.8 Three energy leels A, and C in an aic syse are such ha E A < E < E C. If he waelenghs crrespnding he ransiins C, A and C A are, and respeciely, hen (A) + + = 0 () = + (C) = + (D) = [D] In ers f energy differences, we can wrie E CA = E C + E A. This can furher be wrien as hc hc hc and hence he resul. Q.9 The refracing angle f a pris is A and refracie index is c (A/). The angle f iniu deiain is - (A) (80 A) () (80 A) (C) (90 A) (D) (90 A) Use he pris frula A sin μ A sin c A A A cs sin A A sin sin A sin A sin A A cs = sin. This sugges ha he angles n he w sides are cpleenary, A A ha is, = 90. This can be siplified ge he resul.

5 Q.0 efer he arrangeen f lgic gaes. Fr A A = 0, = 0 and A =, = 0, he alues f upu Y are, respeciely - (A) 0 and () and 0 (C) and (D) 0 and 0 efer he ruh ables f AND, O and NO gaes fr any sandard bk. Q. A plasic ring f radius has a charge + Q disribued unifrly alng ne quarer f is circuference and a charge Q unifrly disribued alng he res f he circuference. The penial n is axis a a disance f is - (A) Q 4 0 () Y 4Q 4 0 Q (C) 4 (D) [C] Using sandard relain, he penial Q Q Q = 4 0 which n siplificain gies he answer. Q. The figure shws fur rienains, a angle wih a agneic field, f a agneic diple wih en M. The agniude f rque () and penial energy (U) is bes represened by 4 Q. A cylindrical essel cnains a liquid f densiy p filled up a heigh h. The upper surface f he liquid is in cnac wih a pisn f ass and area f crss secin A. A sall hle is drilled a he b f he essel. (Neglec he iscus effecs). The speed wih which he liquid ces u f he hle is - (A) (C) gh () g h pa g h (D) pa g h pa Use ernulli's here a he upper surface and a he sall hle. We ge an equain g pgh + where is he speed f A efflux. Sling his we ge he expressin fr speed = g gh gh. A A Q.4 A charged capacir discharges hrugh a resisance. Le U be he energy sred by he capacir and le be he rae a which energy ges dissipaed. Then, he ie cnsan is : 4U U U U (A) () (C) (D) [C] Take he rai f he energy sred in he capacir he pwer dissipaed. ha is, CV U C U C. V Q.5 The fllwing figure shws differen arrangeens f w idenical pieces f plancnex lenses. The refracie index f he liquid used is equal ha f he glass. Then, he effecie fcal lenghs in he hree cases are relaed as (A) =, = 4 and U = U = U = U 4 () = = = 4 and U = U 4, U = U (C) = 4, = and U = U = U = U 4 (D) = = = 4 and U = U = U = U 4 Ne ha he agniude f he rque acing n he diple is = M sin and penial energy is U = M cs. f f f liquid (A) f = f, f = 0 () f f f (C) f = f > f (D) Nne f he abe

6 [D] The fcal lenghs f and f are equal. The arrangeen in he hird case is effeciely a plae and hence has an infinie fcal lengh. Q.6 A lng wire carrying a curren A is placed alng he axis f a lng hllw ube f radius 5 c als carrying a curren f A in he sae direcin. The agneic field a a disance f.5 c fr he axis is : (A) T () T (C) T (D) Zer [A] Ne ha he curren hrugh he wire nly will cnribue he agneic field a a pin inside he hllw ube. Q.7 A Unifr slid sphere f ass has a radius. The graiainal penial a a disance r (< ) fr he cenre f he sphere is : G G (A) ( r ) () ( r ) G G (C) ( r ) (D) ( r ) [C] The graiainal penial a a disance r <, is ade up f w pars ne due he ass f sphere f radius r, say V and ha due he reaining ass, say V. One finds ha GMr G V = and V = ( r ), and hen by adding ne ges he resul. efer any sandard bk. Q.8 The fcal lengh f a cncae irrr is f. An bjec is placed a a disance x fr he fcus and frs a real iage. Therefre, he agnificain (nuerically) is : f f x x (A) () (C) (D) x x f f [A] Since he iage fred is real he bjec us be beynd he fcus. Therefre, aking he bjec disance be (f + x) and using irrr frula, f (f x) we ge he iage disance as and hen x f he agnificain. u x Q.9 A phn f waelengh (less han hreshld waelengh 0 ) is inciden n a eal surface f wrk funcin W 0. The de rglie waelengh f he ejeced elecrn f ass is : hc h (A) h W 0 () hc W 0 h (C) (D) hc hc W 0 h W 0 [] hc Wih usual nain, E k = W0. Als if p is he enu f he phelecrn, E k = p p = Ek. Thus, he de rglie waelengh f he ejeced elecrn h h = which ne subsiuin gies p E k he answer. Q.0 In he fllwing V-T diagra fr a perfec gas, he relain beween p and p is : V p T O (A) p = p () p < p (C) p > p (D) uncerain Ne ha he slpe f he V-T diagra is inersely prprinal pressure p. Q. A phgraphic plae placed a a disance f 0 c fr a pin surce is expsed fr a 4 secnd. If he plae is ed farher away by 0 c, he ie required hae he sae expsure (A) 4 secnd () 6 secnd (C) 8 secnd (D) 64 secnd Accrding he inerse square law, illuinance is inersely prprinal square f he disance. p

7 Q. The lage er a cycle aries as = V 0 sin fr 0 = V 0 sin fr The aerage alue f he lage fr ne cycle is : V (A) 0 V () 0 V (C) zer (D) 0 [D] The lage represens he upu f a full wae recifier whse de cpnen r he aerage V alue is 0. Q. Yung's duble sli experien is firs perfred in air and hen by iersing he whle seup in a liquid. The 0 h brigh fringe when in liquid is fred a he pin where 8 h dark fringe is lcaed when in air. The refracie index f he liquid is : (A).5 (). (C).40 (D).0 D Fringe widh w = where sybls hae heir d usual eanings. Ne ha waelengh in air changes μ in a liquid f refracie index μ. Nw, we can wrie 0 w liq = 7.5 w air liqd aird air = 7.5 air. d d μ This hen gies μ = 0 = Q.4 A spherical shell ade f a eal f densiy reains jus belw he surface f a liquid f densiy. If r and are respeciely he inner and he uer radii f he shell, hen, he rai r is : (A) (C) () (D) Using he law f flaain, we equae he weigh f he bdy he uphrus and ge 4 ( r 4 ) g = g r and he resul fllws. Q.5 A eal srip 6 c lng, 0.6 c wide and 0.7 hick es wih cnsan elciy hrugh a unifr agneic field f inducin 0.9 T direced perpendicular he srip as shwn. A penial difference f.6 μv is induced acrss pins M and N f he srip. Therefre, he speed is : M N (A) 0. /s () 0. /s (C) 0. /s (D) 0.4 /s [] Errr in wrding, quesin deleed. Q.6 The rai f agneic field a he cenre f a curren carrying circular cil is agneic en is x. If he curren and he radius bh are dubled, he alue f his rai wuld be (A) x () 4x (C) x/4 (D) x/8 [D] Ne ha agneic field a he cenre f a curren μ ni carrying cil is 0 and is agneic en r is r nl. Therefre heir rai aries inersely as r. Q.7 A cnducing ring f radius r is placed in a arying agneic field perpendicular he plane f he ring. If he rae a which he agneic field aries is x, he elecric field inensiy a any pin f he ring is - (A) r x () r x/ (C) r x (D) 4 r/x

8 Le E be he elecric field inensiy a a pin n he circuference f he ring. Then, he ef induced = E dl f he ring. Since E where d l is a lengh eleen is cnsan and E dl, he inegral wrks u be E (r). Als he induced d ef is = = r d = r x. Equaing he d d w, we ge he resul. Q.8 Unplarized ligh inensiy f W/ passes hrugh hree plarizers. The ransissin axis f he las plarizer is crssed wih ha f he firs. If he inensiy f ligh eerging u f he hird plarizer is W/, hen he angle beween he ransissin axis f he firs w plarizers is (A) 0 () 0 (C) 45 (D) 60 Le he angle beween he axes f he firs w plarizers be. The inensiy afer he firs plarizer is half f ha inciden n i, ha is 6 W/. The inensiy afer he secnd plarizer will be 6 cs W/. The inensiy afer he hird plarizer can be wrien as = (6 cs ) cs (90 ) since he angle beween he axes f he secnd and he hird plarizers is (90 ). This gies n siplificain, sin () = q = 60 = 0. Q.9 Tw sap bubbles f radii r and r are in cnac wih each her. The radius f curaure f he inerface beween he bubbles is - (A) r () 6 r (C) r (D) r Excess pressure difference acrss he inerface is 4T 4T 4T 4T which us be where is r r 6r he radius f curaure a he inerface. This gies = 6r. Q.40 A radiacie eleen X cners in anher sable eleen Y. Half life f X is hrs. Iniially nly nuclei f X are presen. Afer ie, he rai f nuber f nuclei f X ha f Y is fund be : 8. Therefre, (A) = 9 hrs () = 6hrs (C) = 7.5 hrs (D) is beween 6 hrs and 9 hrs [] Errr in wrding, quesin deleed. SU - AT - A - Q.4 A hp rlls dwn an inclined plane wihu slipping. Then, (A) he inclined plane is sh () he inclined plane is rugh and sill here is n lss f echanical energy (C) he pin f cnac f he hp wih he inclined plane is always a res (D) he linear speeds f differen pins n he ri f he hp are differen [C, D] refer any sandard bk. Q.4 Which f he fllwing phenena is / are relaed he ariain in densiy f aspheric air? (A) irage () in winer sund f a whisle f a railway engine is heard a uch lnger disances (C) winkling f a sar (D) isibiliy f sun fr se ie afer he sunse [A,,C,D] All he phenena re due frain f layers f aspheric air wih differen densiies and hence refracie indices. Q.4 The graph shws he displaceen f a bdy as a funcin f ie. Which f he fllwing is / are he cnclusin? x (A) The graph represens in wih cnsan elciy () The graph represens acceleraed in (C) The bdy ces res afer a lng ie (D) The graph represens a rearded in [C, D] Slpe f he cure a a pin is he elciy which is decreasing in his case and hence he bdy is deceleraing. The graph is rising expnenially and herefre he bdy will ake a lng ie ce res.

9 Q.44 A ransisr is cnneced in cn eier de. The cllecr supply is 0 l and lage drp acrss resisr f k in he cllecr circui is 0.5 l. If he curren gain is is 49, hen (A) he base curren is 50 μa () curren gain is (C) he eier curren is abu 50 μa (D) he base curren is 0 μa [, C] 0.5 The cllecr curren is biusly = A. use he sandard relains fr he curren gains, and he relain beween he =. Als ne ha I E = I + I C. Q.45 The ariain f graiainal field inensiy wih disance fr he cenre f a bdy is shwn in he graph fr which ne can cnclude ha E g [A,, C] Since in case f a resisr he lage and he curren are in phase, pin (d) is n pssible. Due reacie cpnen capacir her pins gien are pssible. Q.47 A persn is siing in a ing rain and is facing he engine. He sses up a cin which falls behind hi. He cncludes ha he rain is ing - (A) frward wih increasing speed () frward wih decreasing speed (C) backward wih increasing speed (D) backward wih decreasing speed [A, D] Only in case f frward accelerain and backward decelerain is he gien bserain pssible. Q.48 Fr an LC circui A C E g 4 O (A) ariain f graiainal field inensiy is due he spherical ass bdy f radius () E g r fr r < (C) he separain f w pins and is 9/4 (D) he separain f w pins and is /4 [A, ] efer any sandard bk. Q.46 When an alernaing curren flws hrugh a circui cnsising f a resisr in series wih a capacir, during he cycle a se insan i is pssible hae - (A) lage acrss he circui zer bu curren hrugh i n zer () curren hrugh he circui zer bu he lage acrss i n zer (C) curren hrugh he capacir n zer bu he lage acrss i zer (D) curren hrugh he resisr n zer bu he lage acrss i zer r D O (A) A and represen and Z respeciely () A and represen Z and respeciely (C) A,, C and D represen Z, X, and X C respeciely (D) fr =, he phase difference beween curren and lage beces zer [C, D] Ne ha is independen f, X L direcly prprinal and X C inersely prprinal. Again Z has a axiu r a iniu alue a = a which he lage and he curren are in phase. Q.49 A furnace has a w layered wall as shwn scheaically. Each layer has he sae area f crss secin. The eperaure a he inerface f w layers can be reduced by i 0 inner layer uer layer 800 C 80 C k i C k 0

10 (A) increasing he heral cnduciiy f uer layer () decreasing he heral cnduciiy f inner layer (C) by increasing he hickness f inner layer (D) by decreasing he hickness f uer layer [A,, C, D] ae f hea flw H = which l l 0 KA K 0A 800 is als equal. Using hese w l KA 70 relains we ge, = 800. Thus K l 0 K 0l ne can reduce he eperaure a he inerface by any f he fur pins gien. Q.50 Siple pendulus and hae lenghs l = 80 c and l = 00 c respeciely. The bbs are f asses and. Iniially bh are a res in equilibriu psiin. If each f he bbs is gien a displaceen f c, he wrk dne is W and W respeciely. Then (A) W > W if = () W < W if = 5 (C) W = W if 4 (D) W = W if [A, D] Wih usual nain, he heigh hrugh which he 4 5 bb falls is h = l( cs) = l sin l since is sall. Therefre, we can wrie 4 h = l l a l =.E. = gh = a. Thus, he wrk dne W l ga W l l = AT Marks : 60 * All quesins are cpulsry. * All quesins carry equal arks Q.5 Assue ha a cnsan pwer is supplied an elecric rain and i is fully used in acceleraing he rain. Obain relain giing he elciy f he rain and disance raeled by i as funcins f ie. wer = cnsan, herefre = F F = d = d. Inegraing his we ge dx =. Wriing he elciy as and d furher inegraing, we ge he expressin fr he disance x = Q.5 A blck f ass.5 kg ress n a rugh hriznal surface. A hriznal frce applied he blck increases unifrly fr 0 5 N in 5 secnd. Deerine elciy and displaceen f he blck afer 5 secnd. Use μ s = 0.6 and μ k = 0.5 and g = 0 /s. Wih usual nain, F s = μ s N = 9N and F k = μ k N = 7.5 N. Applied frce rises F s = 9 N a = s. Therefre, fr s, = 0 and s = 0. Fr s, ne frce n he blck is ( 7.5), d d ha is = 7.5 = 5 d d = 5 + A. Here =.5 kg. Nw, a = s, = 0, gies A = 6. Wih his we ge fr s, = Therefre, a = 5 s, = 6 /s. Fr ds he equain fr, we ge = s = d Again a = s, s = 0, giing 9 =. Wih his we ge, s = 5 4 s = = Hence a = 5 s,

11 Q.5 A wer used fr pwer ransissin leaks a curren in he grund. Assue ha he curren spreads unifrly (heispherically) in he grund. Le p be he resisiiy f he grund and r be he disance fr he cenre f he wer (assued be rd). The lwer end f he rd is spherical wih radius b. Deerine () curren densiy as a funcin f r, () agniude f elecric field a a disance r. and () penial difference beween he lwer end f he rd and a pin disance r. wer efer he figure. Wih usual nain, we hae = qv = qv. Again, = q =. Eliinaing fr he w q relains, we ge l l q V sin = = 0 O V. Nw, sin = q. Subsiuing he alues gies b r inside grund Use I = J da where curren densiy ecr J is parallel he area eleen da f he heispherical surface. When inegraed, he area ces u be r. This gies he curren I densiy direced radially uward a any r pin. Using icrscpic fr f Oh's law J = E where s is he cnduciiy, we ge he agniude f J I elecric field E = where we hae used r J =. Nw, deerine he penial dv difference we use he relain E r = dv dr = Edr. Subsiuing he alue f E and inegraing beween he liis b and r, we ge he penial difference = I r b Q.54 An alpha paricle is acceleraed hrugh a penial difference f 0 kv. Then i eners in a regin f ranserse agneic field f inducin 0.0 T exended up a disance f 0.0. Deerine he angle hrugh which he alpha paricle deiaes. (ass f he alpha paricle = kg) q Q.55 A hin plancnex lens f fcal lengh f is cu alng he axis in w hales. The w hales are placed a a disance d fr each her as shwn. The iages fred by he w hales lie in he sae plane. The disance beween he bjec plane and he iage plane is.8. The agnificain prduced by ne f he hales is. Deerine f, d and he agnificain prduced by he her half. Obiusly L frs an iage wih agnificain = u s ha = u. Again u + =.8 giing u = 0.6 and =.. Using lens frula we ge f = 0.4. Nw, fr lens L, u = d and =. d. Using hese alues and als f = 0.4, we ge d (d 0.6) = 0 r d = 0.6. Furher he agnificain prduced by L is 0.6 =.. bjec plane d L L iage plane