Solu tion Ans. 5. and v = 2R 2 O M. 1 f 1 1 R R. f = 40 cm 1 2 = ( 1)

Transcription

1 \\\\\\\\\\\\\\ J-Physics ns..5 For cas (a) v =, v v and v = m m= = µ For cas (b) v = and v = m µ = m Thrfor µ xampl#7 µ =.5 In figur, L is half part of an quiconvx glass lns ( =.5) whos surfacs hav radius of curvatur = 4 cm and its right surfac is silvrd. Normal to its principal axis a plan mirror M is placd on right of th lns. Distanc btwn lns L and mirror M is b. small objct O is placd on lft of th lns such that thr is no parallax btwn final imags formd by th lns and mirror. If transvrs lngth of final imag formd by lns is twic that of imag formd by th mirror, calculat distanc 'a' in cm btwn lns and objct. O a b M ns. 5 Distanc of imag of objct O from plan mirror = a + b. Sinc, thr is no parallax btwn th imags formd by th silvrd lns L and plan mirror M, thrfor, two imags ar formd at th sam point. Distanc of imag = (a + b) bhind lns. Sinc, lngth of imag formd by L is twic th lngth of imag formd by th mirror M and lngth of imag formd by a plan mirror is always qual to lngth of th objct, thrfor, transvrs magnification producd by th lns L is qual to.sinc, distanc of objct from L is a, thrfor, distanc of imag from L must b qual to a. (a + b) = a b = a Th silvrd lns L may b assumd as a combination of an qui convx lns and a concav mirror placd in contact with ach othr co axially as shown in figur. Focal lngth of convx lns f is givn by \\\\\\\\\\\\\\ f = ( ) For concav mirror focal lngth, f m = = cm 56 f = 4 cm Th combination L bhavs lik a mirror whos quivalnt focal lngth F is givn by F f f F = cm, m Hnc, for th combination u = a, v = +a, F = cm Using mirror formula, a = 5 cm v u F NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65

2 J-Physics Distanc of ird as sn by fish x f = d + h y diffrntiating d(x f ) dh d(d ) dt dt dt h v F = 6 cm/s dh d(d) cm / s, ( ) 4 cm / s, dt dt 3 d v F = d(d) dh dt dt (3) 8 cm/s d(d) dt (for fish imag aftr rflction = ) 3 + () = 3 cm/s Similarly spd of imag of bird 4 cm/s xampl#5 In th shown figur th focal lngth of quivalnt systm in th form of 5x 3. Find th valu of x. ns. 3 f ; 6 3 f 5 and 8 3 f NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p f f f f 5 = 3 = 5x 3 x= xampl#6 3 Quartr part of a transparnt cylindr of radius is kpt on a horizontal floor and a horizontal bam of light falls on th cylindr in th two diffrnt arrangmnt of cylindr as shown in th figur (a) & (b). In arrangmnt (a) light convrgs at point D, which is at a distanc /m from. nd in arrangmnt (b) light convrgs at point, which is at a distanc /(m ) from. Find out th rfractiv indx of th matrial. (a) /m D 55 (b) m-

3 J-Physics xampl#3 olumn-i contains a list of mirrors and position of objct. Match this with olumn-ii dscribing th natur of imag. olumn I olumn II () F (P) ral, invrtd, nlargd () (Q) virtual, rct, nlargd () () virtual, rct, diminishd (D) F (S) virtual, rct ns. () P (b)s () S (D) QS xampl#4 bird in air is diving vrtically ovr a tank with spd 5 cm/s, bas of tank is silvrd. fish in th tank is rising upward along th sam lin with spd cm/s. Watr lvl is falling at rat of cm/s. [Tak : watr = 4/3] olumn I (cm/s) olumn II () Spd of th imag of fish as sn by th bird dirctly (P) 8 () Spd of th imag of fish formd aftr rflction in (Q) 6 th mirror as sn by th bird () Spd of imag of bird rlativ to th fish looking upwards () 3 (D) Spd of imag of bird rlativ to th fish looking (S) 4 downwards in th mirror ns. () (Q) ; () () ; () (P) ; (D) (S) Distanc of fish assn by bird x f = h + d 54 NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65

4 J-Physics xampl# 9 to Thr is a sphrical glass ball of rfractiv indx and anothr glass ball of rfractiv indx insid it as shown in figur. Th radius of th outr ball is and that of innr ball is. ray is incidnt on th outr surfac of th ball at an angl i. r i r O D i 9. Find th valu of r () sin i sin () sin sin i () sin sin i (D) sin sin i. Find th valu of i () sin i sin sin i () ] sin () sin i sin (D) sin i sin. Find th valu of r () 9. ns. () sin sin i sin r = sin i r =. ns. () () sin sin sin i sin i sin r sin(8 i ) Using sin rul sin i = sin r =. ns. () sin i = sin r ; sin i = sin r ; r = sin sin i xampl# () sin sin i sin i (D) i sin sin sin i sin i onsidr a an quilatral prism of glass 3 placd in watr 4 3 watr =4/3 NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65 olumn-i glass =3/ 53 olumn-ii () FG is paralll to (P) Maximum dviation () i = 9 (Q) Minimum dviation 9 () i = i = sin - 6 () TI will tak plac at surfac (D) F is prpndicular to (S) No TI will tak plac at surfac t minimum dviation i = i, F ; t maximum dviation i = 9 or i =9 For i =, TI will not tak plac at ns. () QS, () PS, () QS, (D) S

5 J-Physics 3. ns. () Tim t = distanc spd = Y x x Y 4. ns. () For last tim dt dx = x Y x 5. ns. () c x x Y = sin sin xampl# 6 to 8 On hard and stormy night you find yourslf lost in th forst whn you com upon a small hut. ntring it you s a crookd old woman in th cornr hunchd ovr a crystal ball. You ar about to mak a hasty xit whn you har th howl of wolvs outsid. Taking anothr look at th gypsy you dcid to tak your chancs with th wolvs, but th door is jammd shut. signd to a bad situation you approach hr slowly, wondring just what is th focal lngth of that nifty crystal ball. 6. If th crystal ball is cm in diamtr with.i. =.5, th gypsy lady is. m from th ball, whr is th imag of th gypsy in focus as you walk towards hr? () 6.9 cm from th crystal ball () 7.9 cm from th crystal ball () 8.9 cm from th crystal ball (D) Non of ths 7. Th imag of old lady is () ral, invrtd and nlargd () rct, virtual and magnifid () rct, virtual and small (D) ral, invrtd and small 8. Th old lady movs th crystal ball closr to hr wrinkld old fac. t som point you can no longr gt an imag of hr. t what objct distanc will thr b no chang of th gypsy formd? () cm () 5 cm () 5 cm (D) Non of ths 6. ns. ().5.5 For rfraction at st surfac v 36cm v for rfraction at nd surfac 7. ns. (D) v v v Total magnification = m m = u v u v 6.9cm v (36 ).5 8. ns. () t this point imag will formd at infinity = ngativ 5 Lady cm.5.5 For rfraction at scond surfac v 3cm v x cm For rfraction at first surfac.5.5 x 5cm x () =cm () () () NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65

6 J-Physics ns.() as I ms 5ms v 5i, ˆ v 5i ˆ v om Im I as II ms 5ms v 5i, ˆ v 5i ˆ v ms om Im I as II ms 5ms v 5i, ˆ v 5i ˆ v ms om Im I as IV ms 5ms v 5i, ˆ v 5i ˆ v ms om Im I O v v v 5 or m/s I m o xampl# 3 to 5 ray of light travlling with a spd c lavs point shown in figur and is rflctd to point. Th ray striks th rflcting surfac at a distanc x from point. ccording to Frmat's principl of last tim, among all possibl paths btwn two points, th on actually takn by a ray of light is that for which th tim takn is th last (In fact thr ar som cass in which th tim takn by a ray is maximum rathr than a minimum). 3 Y Y x 3. Find th tim for th ray to rach from point to point. NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65 () Y x x Y c () c 4. Undr what condition is tim takn last? 5 () Y c Y c (D) x c () () x x () Y =Y (D) all of ths 5. Which of th following statmnt is in accordanc with Frmat's principl () ray as it movs from on point to anothr aftr rflction taks shortst possibl path () ray as it movs from on point to anothr aftr rflction taks longst possibl path () ray as it movs from on point to anothr taks shortst possibl tim (D) ray as it movs from on point to anothr taks longst possibl tim

7 J-Physics xampl# ray of light is incidnt in situation as shown in figur. 3 = =4 3 Which of th following statmnts is/ar tru? () If = 3. thn th angl of dviation is zro () If =.8 thn th angl of dviation is 6 () If =.8 thn th angl of dviation is (D) If =.8 thn th angl of dviation is 6 ns.() 3 = =4 3 sin 3 = sin = 3 sin = sin = sin =9 and For <, TI will tak plac at first surfac. 3 = < =4 3 3 = xampl# fish lis at th bottom of a 4m dp watr lak. bird flis 6 m abov th watr surfac and rfractiv indx of watr is 4/3. Thn th distanc btwn () ird and imag of fish is 9 m () Fish and imag of bird is 8m 5 () Fish and imag of bird is m (D) Fish and imag of bird is m For a bird, fish appars 3 m blow th watr surfac and for fish, bird appars 9m abov th surfac. xampl# ns. () plan mirror and an objct has spds of 5 m/s and m/s rspctivly. If th motion of mirror and objct is along th normal of th mirror thn th spd of imag may b : () m/s () m/s () m/s (D) 5 m/s NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65

8 J-Physics x amp l#7 man of hight m stands on a straight road on a hot day. Th vrtical tmpratur in th air rsults in a variation of rfractiv indx with hight y as = (+ ay) whr is th rfractiv indx of air nar th road and a= 6 /m. What is th actual lngth of th road, man is abl to s () m () 39 m () infinit distanc (D) Non of ths ns. () sin = sin9 = ut x amp l#8 sin = ay m dx y tan dx (dy) x dy m dy ay a y a systm of coordinats is drawn in a mdium whos rfractiv indx varis as, whr y y and = for y < as shown in figur. ray of light is incidnt at origin at an angl 6 with y axis as shown in th figur. t point P ray bcoms paralll to x-axis. Th valu of H is :- dy dx x 9 y H P 6 O = x / () 3 ns. () sin sin () 3 / () 3 / at origin x =, y = = & = 6 (D) 4 3 / NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65 x amp l#9 at point P : = 9 sin6 sin9 ray of light is incidnt along a vctor th rflctd ray can b () ˆi ˆj kˆ 3 () ˆi ˆj kˆ ccording to law of rflction so ˆ ˆ.n ˆi ˆj kˆ ˆr ± 3 3 ˆ i 3 3 y y 3 ˆi ˆj kˆ on a plan mirror lying in y z plan. Th unit vctor along ˆr ˆ.n ˆ ˆ nˆ Hr ˆ ˆ ˆ 3 = 3i j k 3 or 49 () ˆi ˆj kˆ ˆi ˆj kˆ 3 ˆi ˆj kˆ ê, ˆn ˆi 3 3 / (D) 3i ˆ ˆj kˆ 3 ns. (,D)

9 J-Physics x amp l#5 If x and y dnot th distancs of th objct and imag from th focus of a concav mirror. Th lin y= 4x cuts th graph at a point whos abscissa is cm. Th focal lngth of th mirror is y x () cm () 4 cm () 3 cm (D) can't b dtrmind ns.() For x = cm, y = 4 = 8 cm From Nwton's formula xy = f () (8) = f f = 4 cm x amp l#6 concav mirror forms an imag I corrsponding to a point objct O. Th quation of th circl intrcptd by th xy plan on th mirror is y O (-5,4) I (5,-) x () x + y = 6 () x + y x 6 = () x + y x 5 = (D) x + y x + 5 = ns. () From mirror quation v u f = x 5 + x 5 = f and from m= v ; u 4 x 5 x 5 4 4x = x +5 3x = 5 x = 5 unit O f ntr of circl will b at (,) ( 5,4) y 48 x +5 I (5, ) x 5 f = unit = 4 unit quation of rquird circl (x ) + (y ) = (4) x + y x 5 = x NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65

10 x amp l#3 J-Physics On on boundary of a swimming pool, thr is a prson at point whos spd of running on ground (boundary) is ms, whil that of swimming is 6 ms. H has to rach a point in th swimming pool.th distanc covrd on th boundary so that th tim rquird to rach th point in th pool is minimum, is Swimming Pool () m () 6m () 7m (D) 6 m ns. () x Swimming Pool quird tim 4 x x t For minimum tim dt x= 7m 5 dx O x -x Just lik light, h has diffrnt spds on ground and in watr, so to minimiz th tim, c Frmat's principl must hold good. 6 3 sin x tan x 7m 4 4 x amp l#4 prson has D cm wid fac and his two ys ar sparatd by d cm. Th minimum width of a mirror rquird for th prson to viw his complt fac is () D d () D d 4 () D d 4 (D) D d NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65 ccording to ray diagram : H M' = H & H M' = H = D (D d) = D d H M' M' = D H M' H M' = D = D d = H D d 47 H M' M M' H M ns. (D)

11 J-Physics SOM WOKD OUT XMPLS x amp l# Th corrct mirror imag of th figur givn is :- () () () (D) ns. () x amp l# point objct O can mov along vrtical lin as shown in figur. Whn imag of th objct is first visibl to D thn it is rlasd at t = from rst from. Th tim for which imag is visibl to D is : O L D L vrtical plan mirror () 6L g () L g () 3L g (D) t L/ D 6L quird tim is givn by 3L = gt t g 46 ns. () NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65

12 J-Physics P SYOPI In this cas both nar and far objct ar not clarly visibl. To rmov this dfct two sparat spctacls on for myopia and othr for hyprmtropia ar usd or bifocal lnss ar usd. STIGM TISM x am pl In this dfct y can not s objct in two orthogonal dirction clarly. It can b rmovd by using cylindrical lns in particular dirction. prson can not s clarly an objct kpt at a distanc byond of cm. Find th natur and th powr of lns to b usd for sing clarly th objct at infinity. For lns u = and and v = cm f v cm concav Powr of lns v u f v f P D f x am pl far sightd prson has a nar point of 6 cm. What powr lns should b usd for y glasss such that th prson can rad this book at a distanc of 5 cm. Hr v = 6 cm, u = 5 cm 3 f cm Powr =.33D f v u f in m 3 / 7 NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65 45

13 J-Physics DFTS OF YS MYOPI [or Short sightdnss or Nar sightdnss] Dfctiv-y () orrctd-y () (i) (ii) Distant objct ar not clarly visibl, but nar objct ar clarly visibl bcaus imag is formd bfor th rtina. To rmov th dfct concav lns is usd. Th maximum distanc. Which a prson can s without hlp of spctacls is known as far point. If th rfrnc of objct is not givn thn it is takn as infinity. In this cas imag of th objct is formd at th far point of prson. P P v u f distanc of far point (in m) distanc of objct (in m) f P distanc of far point (in cm) distanc of objct (in cm) LONG SIGHTDNSS O HYPMTOPI Dfctiv-y () I O orrctd-y () (i) Nar objct ar not clarly visibl but far objct ar clarly visibl. (ii) Th imag of nar objct is formd bhind th rtina. (iii) To rmov this dfct convx lns is usd. Nar Point : Th minimum distanc which a prson can s without hlp of spctacls. In this cas imag of th objct is formd at th nar point. If rfrnc of objct is not givn it is takn as 5 cm. P P v u f distanc of nar point (in m) distanc of objct (in m) f distanc of nar point = v, distanc of objct = v, P = +v 44 NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65

14 J-Physics x am pl With diaphragm of th camra lns st at f, th corrct xposur tim is, thn with diaphragm st at f 4. alculat th corrct xposur tim. s xposur tim t and t aprtur f / f / 4 hr t 6 4 t s thn 4 t 4t s t 4 x am pl x am pl good photographic print is obtaind by an xposur of two sconds at a distanc of cm from th lamp. alculat th tim of xposur rquird to gt an qually good rsult at a distanc of 4 cm. W know that th intnsity of light varis invrsly as th (distanc). Whn distanc is doubld, th intnsity bcoms on fourth. So, th tim of xposur should b four tims. Hnc, tim of xposur = 4 = 8 s Photograph of th ground ar takn from an aircraft, flying at an altitud of m, by a camra with a lns of focal lngth 5 cm. Th siz of th film in th camra is 8 cm 8 cm. What ara of th ground can b photographd by this camra at any on tim. s hr u = m, f =.5m, so from lns formula, v u f as v.5 v w hav v =.5m = 5 cm = Now as in cas of a lns, v.5 m u 4 3 So I = (ma) (mb) = m [ = ab] NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65 x am pl I 8cm 8cm m / 4 3 = (7 m 7 m) Th propr xposur tim for a photographic print is s at a distanc of.6 m from a 4 candl powr lamp. How long will you xpos th sam print at a distanc of. m from a candl powr lamp? In cas of camra, for propr xposur I D t = I D t s hr D is constant and I = (L/r ); L r L 4 t t So t t 6 s.6. r 43

15 J-Physics x am pl tlscop consisting of an objctiv of focal lngth 6 cm and a singl lns ypic of focal lngth 5 cm is focussd at a distant objct in such a way that paralll rays mrg from th y pic. If th objct subtnds an angl of at th objctiv, thn find th angular width of th imag. f f 6 f f 5 MP 4 x am pl Th focal lngths of th objctiv and th y pic of an astronomical tlscop ar 6 cm and 5 cm rspctivly. alculat th magnifying powr and th lngth of th tlscop whn th final imag is formd at (i) infinity, (ii) last distanc of distinct vision (5 cm) (i) Whn th final imag is at infinity, thn : f MP = f = 6 = and lngth of th tlscop is L = f 5 + f = = 65 cm (ii) For last distanc of distinct vision, th magnifying powr is : LNS M f f f D MP 4.4 Now f v u 5 5 u u 5 5 u = 4.7 cm u = 4.7 cm Th lngth of tlscop in this position is L = f + u = = 64.7 cm Thr is a convx lns whos aprtur and distanc from th film can b adjustd. Objct is ral and placd btwn and F, so th imag is ral, invrtd diminishd and btwn F and F. aprtur O film F F F I F shuttr imag If I is th intnsity of light, S is th light transmitting ara of lns and t is th xposur tim, thn for propr xposur,i S t = constant light transmitting ara of a lns is proportional to th squar of its aprtur D ; I D t = constant If aprtur is kpt fixd, for propr xposur, I t = constant, i.., I t = I t If intnsity is kpt fixd, for propr xposur, D t = constant Tim of xposur (aprtur)... (i) Th ratio of focal lngth to th aprtur of lns is calld f numbr of th camra, f numbr = focal lngth aprtur prtur f 4 numbr... (ii) From quation (i) and (ii) Tim of xposur (f numbr) NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65

16 J-Physics NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65 (i) h ' visual angl with instrumnt ( ) f f MP MP h visual angl for unaidd y ( ) h ' u u If th final imag is at infinity v =, u = v u f u f. So MP (ii) If th final imag is at D : v = D u = v f f 4 and lngth of th tub L = f + f f D u f u f D f D So f f f MP u f D Lngth of th tub is L f u S. om p ou n d M icros cop No.. It is usd to incras visual angl of nar tiny objct.. In it fild and y lns both ar convrgnt, of short focal lngth and aprtur. 3. Final imag is invrtd, virtual and nlargd and at a distanc D to from th y. 4. MP dos not chang apprciably if objctiv and y lns ar intrchangd as [MP ~ (LD / f f )] 5. MP is incrasd by dcrasing th focal lngth of both th lnss. 6. P is incrasd by dcrasing th wavlngth of light usd. sin P S. s tron om ical Tls cop No.. It is usd to incras visual angl of distant larg objcts.. In it objctiv lns is of larg focal lngth and aprtur whil y lns of short focal lngth and aprtur and both ar convrgnt. 3. Final imag is invrtd, virtual and nlargd at a distanc D to from th y. 4. MP bcoms (/m ) tims of its initial valu if objctiv and y lnss ar intrchangd as MP ~ [f / f ] 5. MP is incrasd by incrasing th focal lngth of objctiv lns and by dcrasing th focal lngth of ypic 6. P is incrasd by incrasing th aprtur of objctiv. D P. x am pl small tlscop has an objctiv lns of focal lngth 44 cm and an ypic of focal lngth 6. cm. What is th magnifying powr of th tlscop? What is th sparation btwn th objctiv and th ypic? Whn final imag is formd at infinity. Hr, f = 44 cm; f = 6. cm, MP =?, L =? MP = f 44 4 f 6. and L = f + f = = 5. cm x am pl Diamtr of th moon is km and its distanc from arth is km. It is sn by a tlscop whos objctiv and ypic hav focal lngths 4m and cm rspctivly. What will th angular diamtr of th imag of th moon. f f. ngl subtndd by th moon at th objctiv = 3.8 MP =.9 radian. Thus angular diamtr of th imag = MP visual angl = 4.9 =.36 radian =

17 J-Physics (ii) Whn final imag is formd at infinity u f v u f u f v D f D f v D h D MP u f f u f f f h f. Lngth of th tub L = v + f Sign convntion for solving numrical u = v, v = +v, f = +v, u = v, v = v, f = +v, m = v, m = +v, M = v x am pl thin convx lns of focal lngth 5 cm is usd as a simpl microscop by a prson with normal nar point (5 cm). What is th magnifying powr of th microscop? Hr, f = 5 cm; D = 5 cm, M =? D 5 MP 6 f 5 x am pl compound microscop consists of an objctiv lns of focal lngth. cm and an y pic of focal lngth 6.5 cm, sparatd by a distanc of 5 cm. How far from th objctiv should an objct b placd in ordr to obtain th final imag at (a) th last distanc of distinct vision (5 cm) (b) infinity? Hr, f =. cm; f = 6.5 cm, u =? (a) 4 5 v = 5 cm v u f u v f s distanc btwn objctiv and y pic = 5 cm; v = 5 5 = cm u = 5 cm 5 u.5 cm v u f u v f 4 v D 5 Magnifying powr = u f (b) v =, u = f = 6.5 cm v = = 8.75 cm u.59cm v u f u v f v D v D Magnifying powr = 3.5 u f u u STONOMIL TLSOP O " " f F F v 4 ' ' tlscop is usd to s distant objct, objctiv lns forms th imag '' at its focus. This imag '' acts as a objct for ypic and it forms final imag "". f u NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65

18 J-Physics x am pl man with normal nar point 5 cm rads a book with small print using a magnifying glass, a thin convx lns of focal lngth 5 cm. (a) What is th closst and farthst distanc at which h can rad th book whn viwing through th magnifying glass? (b) What is th maximum and minimum MP possibl using th abov simpl microscop? (a) s for normal y far and nar point ar and 5 cm rspctivly, so for magnifir v max = and f u v u f / v v min = 5 cm. Howvr, for a lns as So u will b minimum whn v = minimum = 5 cm i.. min u cm 5 / 5 6 ns u will b maximum whn v = maximum = i.., u max = 5 5 = 5 cm (b) So th closst and farthst distanc of th book from th magnifir (or y) for clar viwing ar 4.7 cm and 5 cm rspctivly. s in cas of simpl magnifir MP = (D/u). So MP will b minimum whn u = max = 5 cm 5 D MP min 5 5 and MP will b maximum whn u = min = (5/6) cm 5 D MP 6 max 5 / 6 OMPOUND MIOSOP ompound microscop is usd to gt mor magnifid imag. Objct is placd infront of objctiv lns and imag is sn through y pic. Th aprtur of objctiv lns is lss as compar to y pic bcaus objct is vry nar so collction of mor light is not rquird. Gnrally objct is placd btwn F F du to this a ral invrtd and magnifid imag is formd btwn F. It is known as intrmdiat imag ''. Th intrmdiat imag act as a objct for y pic. Now th distanc btwn both th lns ar adjustd in such a way that intrmdiat imag falls btwn th optical cntr of y pic and its focus. In this condition, th final imag is virtual, invrtd and magnifid. y lns NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65 objct lns objct h F " final imag F 39 ' " Total magnifying powr = Linar magnification angular magnification MP = m m = (i) Whn final imag is formd at minimum, distanc of distinct vision. v D f D f v D h D u f f u f f f h f MP Lngth of th tub = v + u v u D u

19 J-Physics LT L HOM TI TION s th focal lngth of th lns varis from color to color, th magnification m = f u f producd by th lns also varis from color to color. Thrfor, for a finit siz whit objct, th imags of diffrnt colors formd by th lns ar of diffrnt sizs. Th formation of imags of diffrnt colors violt rd in diffrnt sizs is calld latral chromatic abrration. Th V h V h F V V f diffrnc in th hight of th rd imag and th violt imag V V is known as latral chromatic abrration. L = h h V HOM TISM latral chromatic abrration If two or mor lns combind togthr in such a way that this combination produc imag at a sam point thn this combination is known as achromatic combination of lnss. ' f + = f f' f f f y y For combination of lns. OPTIL INSTUMNTS F f f (pply sign convntion in numrical) Simpl microscop Whn objct is placd btwn focus and optical cntr a virtual, magnifid and rct imag is formd h' h I F h O F Magnifying powr (MP) = (i) Whn th imag is formd at infinity : visual angl with instrumnt ( ) maximum visual angl for unaidd y ( ) MP by lns quation u f v u f u f So MP (ii) If th imag is at minimum distanc of clar vision D : D u f u D f Multiplying by D both th sids [v = D and u = v] D D D D MP u f u f 38 D u D f h u h D D u NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65

20 x am pl J-Physics Th rfractiv indics of flint glass for rd and violt colours ar.644 and.664. alculat its disprsiv powr. Hr, r =.644, v =.664, =? Now v r y v r y.35 x am pl In a crtain spctrum producd by a glass prism of disprsiv powr.3, it was found that r =.645 and v =.665. What is th rfractiv indx for yllow colour? Hr, =.3, r =.645 v =.665, y =? v r y y.3.3 v r.645 y = =.645 x am pl combination of two prisms, on of flint and othr of crown glass producs disprsion without dviation. Th angl of flint glass prism is 5. alculat th angl of crown glass prism and angular disprsion of rd and violt. ( for crown glass =.5, for flint glass =.65, for crown glass., for flint glass =.3). Hr, = 5, ' =?, =.3, ' =., =.65, ' =.5, For no dviation, + ' = ( ) + (' )' = (.65 )5 + (.5 )' = ' =.65 5 = Ngativ sign indicats that two prisms must b joind in opposition. Nt angular disprsion ( v r ) + (' v ' r )' = ( ) + ' (' )' =.3 (.65 )5 +. (.5 ) ( 8.75 ) HOM TI TION = =.975 NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65 Th imag of a objct in whit light formd by a lns is usually colord and blurrd. This dfct of imag is calld chromatic abrration and ariss du to th fact that focal lngth of a lns is diffrnt for diffrnt colors. For a singl lns f and as of lns is maximum for violt whil minimum for rd, violt is focusd narst to th lns whil rd farthst from it. It is dfct of lns. Longitudinal or xial hromatic brration 37 whit light O violt rd violt F V rd f f Y = f Whn a whit objct O is situatd on th axis of a lns, thn imags of diffrnt colors ar formd at diffrnt points along th axis. Th formation of imags of diffrnt colors at diffrnt positions is calld 'axial' or longitudinal chromatic abrration. Th axial distanc btwn th rd and th violt imags I I V is known as longitudinal abrration. Whn whit light is incidnt on lns, imag is obtaind at diffrnt point on th axis bcaus focal lngth of lns dpnd on wavlngth. f f > f V f f V = f y xial or longitudinal chromatic abrration If th objct is at infinity, thn th longitudinal chromatic abrration is qual to th diffrnc in focal lngths (f f V ) for th rd and th violt rays. Y F

21 J-Physics DISPSIV POW () It is ratio of angular disprsion () to man colour dviation ( y ) Disprsiv powr ( V ) V V ( ) fractiv indx of man colour OMINTION OF PISM y y y y Dviation without disprsion ( = ) y V. Disprsiv powr dpnds only on th matrial of th prism. Two or mor than two thin prism ar combind in such a way that dviation occurs i.. mrgnt light ray maks angl with incidnt light ray but disprsion dos not occur i.., light is not splittd into svn colours. Total disprsion = = = ( V ) + (' V ' )' For no disprsion = ; ( V ) + (' V ' )' = Thrfor, ( ) ' V ' V ' v sign indicats that prism angls ar in opposit dirction. Disprsion without dviation Two or mor than two prisms combin in such a way that disprsion occurs i.., light is splittd into svn colours but dviation do not occur i.., mrgnt light ray bcoms paralll to incidnt light ray. Total dviation ( ) ; + (' )' = ' ' v sign indicats that prism angls ar in opposit dirction. GOLDN KY POINTS 36 whit light W whit light Disprsiv powr lik rfractiv indx has no units and dimnsions and dpnds on th matrial of th prism and is always positiv. s for a givn prism disprsiv powr is constant, i.., disprsion of diffrnt wavlngths will b diffrnt and will b maximum for violt and minimum for rd (as dviation is maximum for violt and minimum for rd). s for a givn prism a singl prism producs both dviation and disprsion simultanously, i.., a singl prism cannot giv dviation without disprsion or disprsion without dviation. x am pl x am pl Whit light is passd through a prism of angl 5. If th rfractiv indics for rd and blu colours ar.64 and.659 rspctivly, calculat th angl of disprsion btwn thm. s for small angl of prism = ( ), = (.659 ) 5 = 3.95 and = (.64 ) 5 =3.5 so = = =.9 Prism angl of a prism is o. Thir rfractiv indx for rd and violt color is.5 and.5 rspctivly. Thn find th disprsiv powr. v r Disprsiv powr of prism y but v r.5.5 y.55 Thrfor W V ' ' whit L V NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65

22 J-Physics x am pl ray of light passs through an quilatral prism such that angl of incidnc is qual of mrgnc and th latr is qual to 3/4 th of th angl of prism. alculat th angl of dviation. fractiv indx of prism is.5. = 6, =.5 ; i = i = 3 4 = 45, =? + = i + i 6 + = = 9 6 = 3 x am pl prism of rfractiv indx.53 is placd in watr of rfractiv indx.33. If th angl of prism is 6, calculat th angl of minimum dviation in watr. (sin 35. =.575) Hr, a g =.33, a w =.53, = 6, m =? sin.53 sin a w g w.5 g a g w.33 m sin( m ) w 6 g sin.5 sin.575 m = =. m = sin (.575) = 35. GOLDN KY POINTS ngl of prism or rfracting angl of prism mans th angl btwn th facs on which light is incidnt and from which it mrgs. If th facs of a prism on which light is incidnt and from which it mrgs ar paralll thn th angl of prism will b zro and as incidnt ray will mrg paralll to itslf, dviation will also b zro, i.., th prism will act as a transparnt plat. If of th matrial of th prism is qual to that of surroundings, no rfraction at its facs will tak plac and light will pass through it undviatd, i.., =. DISPSION OF LIGHT Whn whit light is incidnt on a prism thn it is splittd into svn colours. This phnomnon is known as disprsion. Prism introducs diffrnt rfractiv indx with diffrnt wavlngth s min = ( ) > V So V > m(violt) > m(rd) NGUL DISPSION NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65 It is th diffrnc of angl of dviation for violt colour and rd colour ngular disprsion = V = ( V ) ( ) = ( V ) It dpnds on prism matrial and on th angl of prism = ( V ) whit light ray rd orang yllow grn blu indigo violt 35 whit light ray angular disprsion Y V Y V

23 J-Physics ONDITION OF MINIMUM DVITION For minimum dviation In this condition i = i = i r = r = r and sinc r + r = r + r = r = r min Minimum dviation min = i ; i, r if prism is placd in air ; sin i = sin r angl of dviation min sin min sin sin min sin if angl of prism is small < thn sin min min min = min = ( ) ONDITION FO M XIMUM DVITION/G ZING MGN max i=i g i= =i g =9 i=9 angl of incidnc ngl of incidnc (i g )for grazing mrgnc For i g, = 9 pplying Snll's law at fac µsinr = sinr = µ ; r = sin µ = c i g r r r + r = r = c gain, pplying Snll's law at fac sin i g = µsinr ; sin i g = µsin( c ) sini g = µ[sincos c cossin c ] i g sin µ sin cos as sin c µ, cos c µ µ If i incrass byond i g, r incrass thus r dcrass and bcoms lss than c and ray mrgs. Thus i i g ray mrgs, othrwis TI. max = i g + 9 NO MGN ONDITION Lt maximum incidnt angl on th fac i max = 9 sin 9 = sin r ; sin r sin ; r =...(i) if TI occur at fac thn r >...(ii) r + r =...(iii) from (i) and (ii) r + r > + r + r >...(iv) from (iii) and (iv) sin sin sin sin 34 N r r i r > > NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65

24 P I S M J-Physics prism is a homognous, transparnt mdium (such as glass) nclosd by two plan surfacs inclind at an angl. Ths surfacs ar calld th 'rfracting surfacs' and th angl btwn thm is calld th 'rfracting angl' or th 'angl of prism'. Th sction cut by a plan prpndicular to th rfracting surfacs is calld th 'principal sction' of th prism. prism prism prism i It is not a prism for this inclination principal sction of prism prism = i quilatral prism right angld isoscls prism 9 right angld prism NOD6\:\Data\4\Kota\J-dvancd\SMP\Phy\Unit No-\ay-Optics\ng\. ay thory-part.p65 DVITION PQ = incidnt ray Q S i i r r = fractd ray = mrgnt ray = Prism angl = incidnt angl on fac = mrgnt angl on fac = rfractd angl on fac = incidnt angl on fac ngl of dviation on fac. i r ngl of dviation on fac i r Total angl of dviation i r ) + (i r ) i + i (r + r ) In QO r + r + = 8...(ii) In QO + = 8...(iii) from (ii) and (iii) r + r =...(iv) 33...(i) from (i) and (iv) Total angl of dviation = i + i from Snll's law at surfac sin i = sin r and at surfac sin r = sin i P N T Q i r r i O K N' S