Unit 16 Rays Optics Wave Optics

Transcription

1 Uit 6 Rays Optics Wave Optics

2 SUMMARY The path of the light propagatio is called ray, but a budald of such rays is called beam of light. The relatio betwee focal legth ad radius of curvature is R f (for both the mirror) or R = f. the case of plae mirror, R is ifiite ad therefore its focal legth is also ifiite. u v f R For mirrors, Gauss' equatio is, where, u = object distace, v = image distace, f = focal legth, R = Radius of Curvature. Lateral magificatio for mirrors is give by object. m h' h v u, where, h ' = height of image, h = height of The ratio of the sie of the agle of icidece to the sie of the agle of refractio for the give two media is costat, i.e., si θ si θ = = Costat. where is kow as the refraative idex of medium with respect to medium. For a compoud slab of differet trasparet media geeral form of Sell's Law is writte as: siθ siθ Lateral shift x = t. θ f two plae mirros M ad M are iclied at agle θ, the o. of images form 360 = - θ cocave mirror, whe objects is betwee P ad F, image formed is virtual, ereect ad magified. m is positive. However, whe object lies beyod F, image formed is real ad iverted. m is egative. covex mirror, image is always virtual ad erect, whatever be the positio of the object. Critical agle C si where, = refractive idex medium. As C C. 'C' icreases with temperature. v r v r

3 Refractio from a spherical surface (for les) () For refrectio from rarer to deser medium : () Form deser to rarer medium : Les Maker's Formula is : v = - - f R R For Covex les : R = +, R =, f = + Covave les : R =, R = +, f = u = u v R R Power of les P f whe f = m, P = diopter (D) For Covex les P = +, Covave les P = f two leses are i cotact coaxilly, (i) (ii) P P P (iii) m m m f f f For Prism equatio is give by δ = i + e A or A+δ = i + e At miimum agle of deviatio, δ m = i A. i e For thi prism m A() A δ si m A si Newto's formula f = x.x The relatio betwee δ, A ad is : δ = A( ) Agular disperso, θ δv δ r (v r )A δv -δr V r Dispersive power ω = =, Where, δ (i) Resolvig power of huma eye = ' (ii) R.P. of Microscope = siθ λ D (iii) R.P. of Telescope =..λ = + V r 3

4 WAVE OPTCS Problem Solvig Skills : () Resultat itesity R a b abcos + + cos f 0 ÜÜå = cos 4 0 cos () Phase differace x Form = + + cos Whe cos = + max cos = max mi mi f the Sources are icoheret, = + W f W ad W are widths of two Slis the, a W b the iterferce patter max mi youg's double slit experimet (a) Positio of bright friges = a+b a - b where a, b = Amplitude. D x λ (where = 0 for ceteral frige) d (b) Positiio of dark friges x d λd (c) Width of each bright friges = width of each darkfriges β x λd d 4

5 (d) whe etire apparatus is immersed i a medium of refractve idex, frige width becomes ' ' λ D λd x β x ' β d d (e) Agular frige width β λ D d (f) frige visibility is V = max mi / max + mi A thickess t of a medium of refractive idex is equivalet to a legth t i vacuum or air. This is called optical path legth. Whe a thi trasperet plate of thickess t ad refractive idex is placed i the path of oe of the iterferig waves, frige width remais uaffected but the etire pater shiffts by D x t. t d Law of Malus : 0 cos Brewster's law : = ta θp the itesity of porlarised light : Accodig to Doppler's effect for light waves 0 where 0 = itesity of upolarsed light ' f f V C where ' f = apparet frequecy of light f = true frequecy of light A symbol of refractive idex is also deoted by µ 5

6 MCQ Questios (). The velocity of light is maximum i a medium of. (A) diamod (B) water (C) glass (D) vaccum (). A light of wavelegth 30 m eters i a medium of refractive idex.6 from the air of refractive idex.0 The ew wavelegth of light i the medium will be m. (A) 50 (B) 400 (C) 30 (D) 0 (3). "Bhautik" rus towards a plae mirror with a speed of 0 ms, what is the speed of his image? (A) 45 ms (B) 0 ms (C) 5 ms (D) 7.5 ms (4). A ray of light is icidet at a agle 30 0 o a mirror, The agle betwee ormal ad reflected ray is. (A) 5 (B) 30 (C) 45 (D) 60 (5). The o. of images formed betwee two parallel plae mirror are. (A) (B) 0 (C) 80 (D) 360 (6). To get five images of a sigle object oe shold have two plae mirrors at a agle of. (A) 36 (B) 7 (C) 80 (D) 30 (7). f a glass rod is immersed i a liquid of the same refractive idex, the it will. (A) appear bet (B) appear loger (C) disappear (D) appear shorter (8). For four differet trasperet medium 4 3. (A) 4 (B) (C) 4 4 (D) 4 (9). A Plae mirror produces a magificatio of. (A) 0 (B) + (C) (D) (0). A ray light passes through four trasperet media with refractive idices,, 3, 4 as show i figure The surfaces of all media are parallel, if the emerget ray DE is parallel of the icidet ray AB we must have E 6

7 (A) (B) 3 4 (C) (D) 4 3 (). A covex les forms a real image of a object for it s two differet positos o a scree if hight of the image i both cases be 6 cm ad 4 cm the height of the object is cm. (A) 4 (B) 4 (C) 8 (D) 8 (). show figure two parallel rays icidet o a mirror they are reflected as paraller rays as show i the same figure what is the ature of the mirror? (A) plae mirror (B) cocave (C) covex (D) plao cocave (3). The power of plae glass is. (A) (B) 0 (C) D (D) 4D (4). A covex les is made up of three diffret materials as show i figure, for poit object placed o its axis, the o. of imges formed are. (A) 4 (B) (C) 3 (D) (5). Two thi leses of focal legths f ad f are coaxially placed icotact with eachother the, the power of combiatio is. (A) f f (B) f f (C) ff f f (D) f f f f (6). f thi prism of 5 gives a deviatio of the the refractive idex of material of prism is. (A).4 (B).5 (C).6 (D).0 (7). t is difficult to see through the fog because (A) light is seattered by the doplets i the fog. (B) fog absorbs light. (C) rafractive idex of fog is ifiity. (D) light suffers totl iteral reffectio. (8). what is the time take i secods to cross a glass plate of thikess 6 mm ad µ =.0 by light? (A) 8 0 (B) 4 0 (C) 0 (D) 60 (9). Which of the followig diagrams shows correctly the dispersio of white light by a prism? (A) (B) (C) (D) 7

8 (0). Read the followig quetios ad choose if. (A) both assertio ad reaso are true ad the reaso is correct explaatio of the assertio. (B) both assertio ad reaso are true but reaso do ot explai the assertio. (C) Assertio is true but the reaso are false. (D) both assertio ad reaso are false. () Assertio : Focal legh of a les for red colour is smaller tha its focal legth for violet colour Reaso : is becuse r V (A) B (B) A (C) C (D) D (). which of the followig cases a ma will ot see image grater tha himself. (A) covex mirror (B) cocave mirror (C) plae mirror (D) oe of these (). A glass slab =.5 of thikess 9 cm is placed over a writte paper what is the Shift i the latters? (A) 6 cm (B) 3 cm (C) cm (D) 0 cm (3). A cocave mirror of focal legth 0 cm forms a virtual image havig twice the liear dimesios of the object, the positio of the object will be cm (A) 7.5 (B) 0 (C) 0 (D) 7.5 (4). experimet to fid focal legth of a cocave mirror a graph is draw betwee the magitude of u ad v. The graph looks like. (A) (B) (C) (D) (5). A mark at the bottom of the liquid appears to rise by 0. m, f depth of the liquid is.0 m the refractive idex of the liquid is. (A).80 (B).60 (C).33 (D). (6). A Soud wave travels from air to water. the agle of icidece is α ad the agle of reflectio is α f the sell's Law is valid the,. (A) α (B) α (C) α (D) α (7)..6 is a refractive idex of plao-covex les, the the redius of curvature of the curved suface is 60 cm. The focal legth of the les is cm (A) 50 (B) 00 (C) 50 (D) 00 (8). Oe covex les ad oe cocave les placed is cotect with eachother. f the ratio of their power is 3 ad focal legth of the combiatio is 30 cm, the idivedual focal legths are. (A) 5 cm ad 0 cm (C) 30 cm ad 0 cm 8

9 (B) 5 cm ad 0 cm (D) 30 cm ad 30 cm (9). A thi prism of 3, agle made from glass of refractive idex.5 is combied with aother thi prism made from glass of refractive idex.3 to produce dispersio without deveatio. what is the agle of Prism of secod prism. (A) 3 (B) 3 (C) 5 9 (D) 5 (30). f a ray of light is icidet o a plae mirror at a agle of 30 the deviatio produced by a plae mirror is. (A) 60 (B) 90 (C) 0 (D) 50 (3). The frequecy of a light wave i a material is H z ad wavelesth is 5000 A. The 8 - refractive idex of material will be ( take c = 3 0 m s ) (A).5 (B).7 (C).33 (D) Noe of these 3. Moo chromatic light of wavelegth 399 m is icidet from air o a water.33 Surface. The wavelegth of refracted light is m (A) 300 (B) 600 (C) 333 (D) f the refractive idex of a material of a equilateral Prism is 3, the agle of miimum deviatio will be. (A) 50 (B) 60 (C) 39 (D) f the critical agle for total iteral reflectio from a medium to vacuum is 30 the velocity of light i the medium is ms ( take c = ms ) (A).00 8 (B).50 8 (C) 0 8 (D) A ray of light passes from glass.5 to medium.60 glass is. (A) 6 si 5 (B) The value of the critical agle of 6 si (C) si 5 (D) si A double covex les of focal legth 6 cm is made of glass of refractive idex.5, The radius of curvature of oe surface is double tha that of the other surface. The value of small radius of curvature is. (A) 6 (B) 9 (C) (D) Whe a ray of light eters i a trasperet medium of refractive idex, the it is observed that the agle of refractio is half of the agle of icidece. The value of agle of icidece will be.

10 (A) cos - (B) cos A prsim of glass is show i figure A, ray icidet ormally o oe face is totally reflected. f θ is 45, the idex of refractio of glass is. (C) si - (D) si - (A) < (B) > (C) = (D) Noe of these 39. A covex les made up of a material of refractive idex is immersed i a medium of refractive idex as show i the figure. The relatio betwee ad is. (A) (B) (C) (D) 40. Two plao covex leses of radius of curvature R ad refractive idex.5 will have equivalet focal legth equal to R, whe they are placed. (A) at distace R (C) at distace R 4 (B) at distace R (D) i cotact with each other 4. A double covex les made of glass of refractive idex.6 has radius of curvature 5 cm each. The focal legth of this les whe immersed i a fluid of refractive idex.63 is. (A) (B) (C) 5 (D).5 4. Oe ray of light suffers miimum deviatio i a equilateral prism P additloal prism Q ad R of idetical show i fiqure. The ray will ow suffer. (A) greater devaitio (C) total iteral reflectio (B) same divaitio as before (D) o devaitio 43. Which of the followig colours is scattered miimum? (A) Violet (B) red (C) blue (D) yellow 44. Agle of miimum devaitio for a prism refractive idex.5 is equal to the agle of the prism The the ' agle of prism give, si (A) 6 (B) 8 (C) 60 (D) a thi prism of glass (a g =.5) which of the followig relatio betwee the agle of miimum deviatio δm ad the agle of refractio r will be correct? (A) δ m r (B) δ m r (C) δ.5 r 0 m (D) δ m r

11 46. A observer look at a tree of height 0 meters away with a telescope of magifyig power 0. To him, the tree appears. (A) 0 times taller (B) 0 times smaler (C) 0 times earer (D) 0 times earer 47. A ormal perso wats to see two pillars at a distat km away separately. The distace betwee two pillars should be approximately. (A) m (B) 3. m (C) 0.5 m (D).6 m 48. Whe the legth of microscope tube icreases, its magifyig power. (A) decreases (B) icreaes (C) does ot chage (D) oe of these 49. The focal legths of objective ad the eye piece of a compoud microscpe are fo ad fe raspectively. The. (A) F o > F e (B) F o < F e (C) F o = F e (D) oe of these 50. The magifyig power of a telescope is 9.0 whe it is focussed for parallel rays, the the dictace betwee its objective ad eye piece is 0 cm The focal legths of leses will be. (A) 5 cm, 5 cm (B) 8 cm, cm (C) 0 cm, 5 cm (D) cm, 9 cm 5. A plao covex les of f = 0 cm is silvered at plae surface New f will be cm (A) 0 (B) 40 (C) 30 (D) A ray of light from deser medium strikes a rarer medium at agle of icidece i. The reflected ad refracted rays make a agle of 90 with each other The agle of reflectio ad refratio are r ad r ' respectively. The crictical agle is. (A) si (ta p) (B) ta (ta r) (C) ta (si i) (D) si (ta r) 53. Relatio betwee critical agle of water C w ad that of the glass C g is. (give, w = 4/3, g =.5) (A) C w < C g (B) C w = C g (C) C w > C g (D) C w = C g = O 54. The radius of curvature of covex surface of a thi plao covex les is 5 cm ad refractve idex of its material is.6 The power of the les will be. (A) 6 D (B) 5 D (C) 4 D (D) 3 D 55. A ray of light passes through a prism havig refractive idex =, Suffers miimum deviatio f agle of icidet is double the agle of refratio withi prism the agle of prism is. (A) 30 (B) 60 (C) 90 (D) A air bubble iside glass slab =.5 appear from oe side at 6 cm ad from other side at 4 cm. The the thikess of glass slab is cm (A) 5 (B) 0 (C) 5 (D) The magifyig power of objective of a compoud microscope is 5.0 f the magifyig power of microscope is 30, the magifyig power of eye piece will be. (A) 3 (B) 6 (C) 9 (D)

12 58. Light of certai colour cotai 000 waves i the legth of mm i air. What will be the wavelegth of this light i medium of refractive idex.5? (A) 000 A o (B) 000 A o (C) 3000 A o (D) 4000 A o 59. each of the followig questios match columm- ad columm- ad select the correct match out of the four give choices. Columm : Columm : (i) Sell's Law (a) Frequecy remais uaffected (ii) vacum (b) = sii/sir (iii) glass (c) v violet = v red (iv) goig form oe medium (d) v violet < v red (A) i a, ii b, iii c, iv d (C) i b, ii c, iii d, iv a (B) i d, ii c, iii b, iv a (D) i c, ii b, iii d, iv a 60. Columm Columm (i) While goig from rarer to deser medium (a) wavelegth charger (ii) While goig from deser to rarer medium (b) (iii) While goig to oe medium to aother (c) Ray beds towards ormal (iv) Refractive idex of medium (d) Ray beds away from ormal (A) i c, ii d, iii b, iv a (C) i d, ii c, iii b, iv a (B) i a, ii b, iii c, iv d (D) i b, ii c, iii a, iv d 6. Columm Columm (i) Mea deviatio (a) A (ii) Agular dispersio (b) C V '- A' 0 - (iii) Dispersive power (c) (v - r )A (iv) Coditio for o deviatio (d) ( )A (A) i c, ii d, iii b, iv a (C) i c, ii b, iii a, iv d (B) i a, ii b, iii c, iv d (D) i d, ii c, iii b, iv d 6. A covex les of glass =.5 has focal lergth 0. m The les is immersed i water of refractive idex.33. The chage i the power of covex les is. (A) 3.7 D (B) 4.6 D (C) 6.44 D (D).86 D 63. For a prism of refractive idex 3, the agle of miimum deviatio is eqviatio is equal to the agle of prism, the agle of the prism is. (A) 60 (B) 90 (C) 45 (D) 80 v r

13 64. A ray of light is icidet ormally o oe of the faces of a solid prism of agle 30 ad refractive idex. The agle of miimum deviatio is. (A) 39 (B) 4 (C) 5 (D) A plao covex les has bee fixed exactly ito a plao cocave les as show i figure. Thier plae surface are parallel to each other. f both the leses are made of differet materials of refractive idices ad, R is the radius of curvature of the curved suface of the les, their focal legth of the combiatio will be. R (A) (B) R (C) R R (D) 66. A cocave mirror has a focal lagth 30 cm The distace betwee the two positio of the object for whi ch image size is double of the object is. (A) 30 cm (B) 5 cm (C) 5 cm (D) 5 cm 67. A cocave les forms the image of a object such that the distace betwee the object ad the image is 0 cm ad the magificatio produced is 4, the focal legth of les will be cm (A) 6. (B).4 (C) 4.4 (D) A prism of certai agle deviates the red ad blue rays by 8 ad respectively. Aother prism of the same prism agle deviates the red ligst at small agle ad made of diffeut materials The dispersive powers of the materials of the prisms are i the ratio. (A) 5:6 (B) 9: (C) 6:5 (D) :9 69. The head light of a jeep are. m apart. f the pupil of the eye of a objerver has a diameter of mm ad light of wavelegth 5836 A is used what should be the maximum distace of the jeep from the observer if two head lights are just seem to be separated apart? (A) 30.9 km (B) 33.4 km (C) 3.34 km (D) 30.9 km 70. The effective focal legth of the les combiatio show i the curved surface of the plao covex leses are cm each ad refractive idex of the material of the les is.5. the refractive idex of liquid is. (A).33 (B).4 (C).53 (D).60 3

14 7. terferece is possible i. (A) light waves oly (C) both light ad Soud waves (B) Soud waves oly (D) oo of these 7. Huygi's wave theory of light ca ot explai pheomia. (A) Diffractio (B) terferece (C) palarizatio (D) Photoelectric effect 73. The correct curve betwee frig width β ad distace betwee the slits d is show below figure is. (A) (B) (C) (D) 74. The frige width for red β r βr β. υ λ r 8000 A ad the frige width for violct βυ λ υ 4000 A the (A) : (B) : (C) : (D) : 75. Wave ligth travels from a optically rarer medium to a optically deser medium its velocity decreaes because of chage i. (A) frequecy (B) wavelesth (C) amplitude (D) phase 76. youg's double slite experimet if the width of rd 3 frige is 0 cm, the the width of th 5 frige will be cm (A) 0 (B) 5 0 (C) 0 (D) The youg's double slit experimet is performed with blue ad with gree light of wavelesths 4360 A ad 5460 A respectively. f x is the distace of th 4 maxima from the cetral oe, the. (A) X blue = X gree (B) X blue > X gree (C) X blue < X gree (D) oe of these 78. The light waves from two coheret sources of same itesity iterfere eachother. The what will be maximam itesity whe miimum itesity is zero? (A) 4 (B) (C) 4 (D) 79. youg's doble Slit experimet the seveth maxima with wavelegth λ, is at a distace d ad the same maxima with wavelegth λ, is at a distace d The d d. (A) (B) 4 (C) (D)

15 80. The wave legth corresspodig to photo is 0.06 A. ts K.E. J. (h = S, c = ms ) (A) (B) (C) (D) youg's double slit experimet, phase diffrece betwee light waves reachig rd 3 bright frige from cetral frige with, is.( λ =5000A ) 8. th (A) zero (B) π (C) 4π (D) 6π bright frige of red light λ 7500 A λ 6000 A. The value of =. Coicides with (A) 8 (B) 4 (C) (D) 83. Which of the followig will udergo maximum diffratio? th bright frige of gree light (A) - particle (B) γ - rays (C) radio waves (D) light waves A Slit of width 0 m is illmiated by light of waveleth 6000 A. The agular width of the cetral maxima is appoximately. (A) 30 (B) 60 (C) 90 (D) The distace betwee the first ad sixth miima i the diffractio patter of a sigle slit, it is 0.5 mm. The scree is 0.5 m away from the Slit. f the wavelegth of light is 5000 A, the the width of the slit will be mm (A) 5 (B).5 (C).5 (D) chage i the polarizatio phyomia of ligst? (A) itesity (B) wavelegth (C) phase (D) frequecy 87. yog's double slit experimet the phase diffrece is costat betwee two sources is π. The itesity at a poit equi distat from the slits i terms of max. itesity 0 is. (A) 3 0 (B) 0 (C) figure youg's double slit experimet Q is the positio of the first bright friges o the right side th of O, p is the frige o the other side as measured from Q f λ = 6000 A 0 the S B will be m (A) (B) (C) (D) (D)

16 89. The two coheret sources of itesity β produce iterferece. The frige visibeility will be (A) β (B) β (C) β β (D) β β 90. Light of wave legth λ is icidet o a slit of width d. The resultig diffractio patter is observed o a scree placed at a distace D. The liear width of the pricipal maximum is equal to the width of the slit, the D =. (A) d λ (B) λ d (C) d λ 9. A polariser is used for. (A) producp polarised light (C) produced upolarised light (B) produced upolarised light (D) oe of these 9. Read the paragraph ad chose the correct aswer of the followig quetios youg exprimet positio of bright friges is give by D d (D) d λ D x λ ad the posito of dark friges is d give by x where =,,3... for first, secod, third bright / dark frige. The λd ceter of the frige patter is bright (for = 0). The width of each briht/dark frige is β, Where d λ = 5000 A 0. (i) f light of wavelegth 6000 A be used i the above experimet the frige width would be mm (A) 0.36 (B) 3 (C) 0.6 (D) 6 (ii) with the light of wavelegth 5000 A, f experimet were carried out uder water of a 4 = 3 the frige width would be (A) zero (B) 3 4 times (C) 4 3 times (D) oe of these 93. The width of a sigle slit, if the first miimum is observed at a agle of with a wavelegth of light 6980 A is mm (A) 0. (B) 0 5 (C) 0 5 (D) a frauhofer diffractio by sigle slit of width d with icidet light of wavelegth 5500 A the first miimum is observed at agle of 30. The first secodary maximum is observed at a agle θ =. (A) si (B) si 3 4 (C) 3 si (D) si The pheomeo of polarisatio of electromagetic waves proves that the electromagetic waves are. (A) mechaical (B) logitudial (C) trasverse (D) oo of these 6

17 96. Light from two coheret Sources of the same amplitude A ad wavelegth λ, illumiates the Scree. The itesity of the cetral maximum is o. f the sources were icoheret, the itesity at the same poit will be. (A) 0 (B) 0 (C) (D) Whe the agle of icidece is 60 o the Surface of a glass slab, it is foud that the reflected ray is completely palarised. The the velocity of light i glass is ms (A) (B) (C) 3 (D) Two beams of Light of itesity ad iterfere to give a iterferece patter. f the ratio of 6 maximum itersity to that of miimum itesity is the 4 = (A) :9 (B) :4 (C) 4: (D) 9: 99. Which of the followig pheomeo is used i optical fibres? (A) Reflectio (B) Scattertig (C) Total iteral reflectio (D) terferece 00. Two beams of light havig itesities ad 4 iterfere to produce a frige patter o a scree. The phase diffrece betwee the resultat itesities at A ad B is. (A) (B) 4 (C) (D) 6 0. A soud source emits soud of 600 Hz frequecy, this soud eters by opeed door of width 0.75 m. Fid the agle o oe side at which fitst miimum is formed. The speed of soud = 300 ms. (A) 84.4 (B) 90 (C) 74. (D) A plae polarised light is icidet ormally o the tourmalie plate. its E vectors make a agle of 45 with the optical axis of the plate. fid the percetage differece betwee itial ad fial maximum values of E vectors. (A) 9% (B) 9% (C) 50% (D) 9% 03. Yog's double slit experimet, the iesity o scree at a poit where path differece is λ, is K, What will be itesity at the poit where path differce is 4 λ (A) K (B) K (C) 4 K (D) zero 04. Ordiary light icidet o a glass slab at the polarisig agle, suffers a deviatio of. The value of agle of refracio i this case is. (A) 44 (B) 34 (C) (D) 05. The ratio of iesities of rays emitted from two differet coheret Sourees is α. For the ierferece patter by them, max mi max mi will be equal to. (A) α α (B) α α (C) α (D) α α 7

18 KEY NOTES D 6 D 5 C 76 A 00 B C 7 B 5 D 77 C 0 D 3 B 8 B 53 C 78 A 0 D 4 D 9 C 54 C 79 D 03 A 5 A 30 C 55 C 80 A 04 C 6 B 3 A 56 C 8 D 05 D 7 C 3 A 57 B 8 B 8 D 33 B 58 D 83 C 9 B 34 B 59 C 84 B 0 C 35 D 60 A 85 B D 36 D 6 D 86 A A 37 A 6 A 87 B 3 B 38 B 63 A 88 C 4 C 39 C 64 D 89 D 5 D 40 D 65 B 90 A 6 A 4 B 66 A 9 A 7 A 4 B 67 C 9(i) A 8 B 43 B 68 C 9(ii) C 9 C 44 B 69 C 93 D 0 D 45 D 70 D 94 B A 46 C 7 C 95 C B 47 B 7 D 96 A 3 C 48 A 73 C 97 B 4 D 49 A 74 A 98 D 5 D 50 B 75 B 99 C 8

19 . use λ. λ' HNTS 5. No of image = Use ho = hh. Use, shift = 5. Here, x h 0 h' h'.5 8 a 6. Here, i = r ad a ( ) w i V V w si i si Now aw si r si ( ii) Va But Vw.6 f 00 cm f Here, P f f 8. Here, f (i) P 3 f f f f 5 cm ad f 0 cm 3 Now, 9. Here, A A A 0.3 A 0 A Here, o 3. Use, v = f λ ad c υ 9

20 36. Use, ( ) f R R R R, R R take R = 4.5 cm 37. Here, i i i si( ) si.cos si i si r si si i cos i cos i i cos 38. Here, i θ c = 45 0 si c The value of critical agle (c) is miimum for its divers the rays,. = - - =.6 - = fa R R Here, fa.5cm Now, f µ = = = fa µ µ.63 f cm 43. wavelegth maximum, Scatterig is miimum A+A A A si si.cos si A = si A A si si 44. Here, A 3 A A cos, = cos (0.75) = 4, A = o o 30

21 45. Here m r ad i (r r ) whe i δ δm the i i r r r i si i i δm i r r r i r si p r 3 = r ( ) r δm = r 46. Here magifyig power is 0 there it ca be see 0 times ear. 47. Use : D d Use 3. m R 0 c m f R R for rarer medium to deser, u v f u υ R f 30 cm f 0 5. fromfig : 90 r 90 r ' 90 r ' 90 r ow si c si i si 90 r si i cos i si c ta i ta r i r C si ta r 53. Here 3 w 4 - Cw si si 48.6 Cg si 4 g Cw Cg 54. Use ( ) f R R f 0.5 m, P 4D 55. Use si i si r si r.cosr cos r si p si r si r 3 cos

22 r 45 A Use Real depth x appertdepth y x y 5 cm ( apperet depth = 6+4=0) 58. Use = Now disa t 5000 A wave No. λ λ' 4000 A a g 6. Here, w g.8 a g Now, (a g ) fa R R 0 R R w fw R R ad g the Pa 5 D ad Pw 0.8 Pa Pw 3.7 D fa 63. Use, A δm si / A cos si A δm = A A 3 cos A Here, i = 90 r =0, r r A, r 30 Now, = si i si r i 45 i e A δ m δ m 5 0 3

23 f f f R R 65. Use F R 66. Here : For Real image u υ, υ = v f 30cm u 45 cm u u 30 For virtul image u u f 30 cm u 5 cm u u 30 u u 3 0 c m 67. Here, m u 4v 68. Use δ V δ V Use 6 : 5 '.λ x dθ = D r if 4 u x u 4x the 0 from figure, 0 = 4x-x, 3x = 0 cm x = cm 3 Now, u4υ = 4x formfig : υ= x 40 u 40 0 ad υ = cm from f 4.4 cm f u υ ' δ 'υ 'v ad ' 3 where r = distat of jeep car f f R For, plao-covex les For, doble covex les 3 f f f 60 f 0 3 r = 3.34 km f R R Now.6 33

24 80. A. Use K-E = hc 8. Use = Here, = ta 8 θ p 3, = c v = 3 0 v 98. From m a x m i = a+ b a-b a Now 9 : b 00. Here, A ad, 3 b = 9 π cos 4 4 cos90 A 5 = cos = 5-4= B A 0. = 0 0 cos θ = B 4 ad E - E 0 = 0.9 = 9% E 0 E E =, = E E 04. from Fig, θp + 90 r θp + r = 90 ad θp - r = r Here ad E α E α E E α α m a x E E α m i α max mi max mi α α 4 α α 34