ET «sc STUDY / PASSAGE BASED QUESTIONS i yllabus lave optics: Wave ont and Huygen's rinciple, reflection rd refraction of lane wave ata lane surface using ave fronts. Proof laws of reflection refraction using sygen's principle. terference, ‘ung's double texperiment d expression fringe width, herent sources d sustained terference of light, fraction due to a agle slit, width of _ ntral maximum Questions 1-10 are Case udy based questions and are compulsory. Attempt rk. Wave Optics | | any 4 sub p, » ny 4sub parts from each question, Each question carries 11 e Intensity of Interference I double slit apparatus is immersed in a liquid of refractive index, u the wavelength of light reduces to i’ and fringe width also reduces to 8’ = © u The given figure shows a double-slit experiment in which coherent monochromatic light of wavelength 7. from a distant source is incident upon the two slits, each of w idth w(w >> 2) and the interference pattern is viewed on a distant screen. A thin piec glass of thickness t and refractive index 1 is placed between one of the slit and the screen, perpendicular to the light path. L e of ee (i) In Young's double slit interference pattern, the fringe width (a) can be changed only by changing the wavelength of incident light (b) can be changed only by changing the separation between the two s (c)_ canbe changed elther by changing the wavelength or by changing the separation between two sources (d) isa universal constant and hence cannot be changed ts (ii) If the width w of one of the slits is increased to 2w, the become the amplitude due to slit (a) 15a (b) af2 (©) 2a (d)_ no change (iii) In YDSE, let A and B be two slits, Films of thicknesses 1, and fy and refractive indices m, and my are placed in front of A and B, respectively. If , ty = tp t,, then the central maxima will ‘A Bh (a) not shift (b) shift towards A (©) shift towards B (d) shift towards A if ty i, and shift towards B if ty < ty(iv) In Young’ e slits. Then '8) Ih Young’s double slit experiment, a third sfit is made in betwee? the double slits. ‘Then e : fringes of unequal width are formed contrast between bright and dark fringes is reduced (©)_ intensity of fringes totally disappears (@)_only bright light is observed on the screen, (©) In Young’s double slit experiment, ifone ofthe sit Iscavered with a microscoPe cover slip, then (a) fringe pattern disappears (b)_ the screen just gets illuminated (© in the fringe pattern, the brightness of the bright fringes will decrease more dark os and the dark fringes will become (a) bright fringes will be more bright and dark fringes will become more dark. | NS Fringe Width Distance between two successive bright or dark fringes is called fringe (n+DAD_mkD _ 2D ay, -y,= @tnan mp 2 B= You ae xima, If whole apparatus is immersed in liquid of rel width, Fringe width is independent of the order of the ma) ractive index u then B = % (fringe width decreases). Angular fringe width (8) Is the angular separation between two consecutive maxima or minii RID In the arrangement shown in figure slit S, and S, are having a variable separation Z. Point © on the screen 83h the common perpendicular bisector of 5,5, and $,S,- Le ls, t ch "le voalet v (i) The maximum numberof possible interference maxima for sit separation equal twice the wavelength in Young's double-slit experiment, is (a) infinite (b) five (o) three aaa _ slit experiment if yellow light is replaced by blue light, the interference fringes become Gi) In Young's double (b) brighter (©) narrower (@) darker (a) wider experiment, i the separation between the slits is halved and the distance between the doubled, then the fringe width compared to the unchanged one will be ' (b) Halved (©) Doubled (a) Quadrupled (ili) In Young’s double slit slits and the screen is (a) Unchanged (ax) When the complete Young’ double sit experiment is immersed in water, the Iringes (a) remain unaltered (b)_ become wider (©) become narrower (a) disappearAM trnge is abserved ona screen kept behind the sts: WP White fringe (b)_ gets displaced fromy its earlier positio? a Diffraction at a Single Siit (Fraunhofer) When light tro o Hight trom a 1 el and a pattern of monochromatic sontree o aMernate bright wears wouitce is incident on a single narrow slit, it gets diffrac i Fight andl dark tring In diffracti " Finges is obtained on sen diffraction Pattern” of single shit Pattern single st tte on screen, called “Ditfraction Patt 8 (1) Central bright trin, secondary bright fringe decreases psity of a with increase in its order, " (1) Central bright tringe ts twice as widh ny other secondary bright or dark fr Viewing sereen (i) A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength 6000 A and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band trom the central bright band is (a) 3mm (ii) In Fraunhofer diffraction pattern, slit width is 0,2 mm and screen is at 2 m away from the lens. IT wavelength of light used is 000 A then the distance between the first minimum on either side the central maximum is (b) 10? m (Q 2x10? m (@) 2x10'm (b) 1.5mm () 9mm (d) 45mm (a) 10'm (iii) Light of wavelength 600 nm is incident normally on a slit of width 0.2 mm. ‘the ‘maxima in the diffraction pattern is (measured from minimum to minimum) (b) 410" rad (©) 24% 10% rad (d) 4.5% 10 Sad angular width of central (a) 610 *rad (is) A ditraction pattern is obtained by using a beam of red ight, What will happen i the re lights replaced by the blue light? re (a) bands disappear (b) bands become broader and farther apart (0) no change will take place (d) diffraction bands become narrower and crowded together (*) “To observe diffraction, the size ofthe obstacle (a) should be 2/2, where 1s the wavelength (0) should be ofthe order of wavelength, (©) has no relation to wavelength. (4) should be much larger than the wavel th vavelengt!—\———~ Interference Fringes {BYoung’s double sit experiment, the width of the central bright fin} Tr atiges on the two sides of the central bright nee, in Siven figure below a seren is placed normal vs setae joing the {0 PO interference pattern consists af concentnn cr ce between the first equal to the distan ige sequal int coherent source S, and S>, The th me The optical path difference at P is 1 2 @ 4 we 20 ‘| ap (b) | a ( d| } (ii) Find the radius of the n'* bright fringe. @ D 11-28) ® b(.-) © yal } (@) of(-2) (iii) If d = 0.5 mm, 3 (d) «fp- 5000 A and D = 100 cm, find the value of n for the closest second bright fringe (a) 888 (b) 830 (©) 914 (d) 998 (iv) The coherence of two light sources means that the light waves emitted have (a) same frequency (b) same intensity (©) constant phase difference (d) same velocity. (*) The phenomenon of interference is shown by (a) longitudinal mechanical waves only (b) transverse mechanical waves only (©) electromagnetic waves only (d) allofthese Ot Maxima and Minima Intensity Amarr tube i ent inthe frm ofa cel fra Rs sho in gure. Two stall oles Sand Dar a the tube a the positions at right angle to each other. A source placed t ¢ Senerates a wave of intensity | re i equally divided into two parts one part travels along the longer path, wha other travels along thechen Path, Both the waves meet at point D wherea detector is placed. along the shorter) Wa maxim, iven bY 11 is formed at ve produced is gi 4 detector, then the ee ‘Magnitude of wavelength 7, of the | fo ™ (a) all of these a ent is 49: 1s then the ratio "to coherent sources used in Young’s double sit experiment maximum intensities in the interference pattern i (a) mR (i) the intensity ratio o between the and minimum @ 1:9 (d) 16:9 () 9:16 (co) 25:16 : (Wi) The maximum intensity produced at Dis given by (a) 4h, : (b) 20, e (ot (d) 31, elength : erence is 7/6 (7. ~ waveleng () In.a Young’ double sit experiment the intensity at a point where the path difference is of the light) is 1. If 1, denotes the ‘maximum intensity, then I/J, is equal (0 1 3 1 d) = @ 5 ty) 8 ©) 4 erence d. After they superpose or emcee res Propagating in the same direction, have a phase differenc Y of the resulting wave will be proportional to xs cos’S (a) cos8 (b) co0s(8/2) (©) cos8/2) AO coe Sources of Light central line are Consider the situation shown in figure. The two slits S, and S, placed symmetrically sound the nailer illuminated by monochromatic light of wavelength 2. The separation between the slits isd The light transmitted by the slits falls on a screen S, place at a distance D from the sits. The slits Sis at the central line a is ata distance from S,, Another screen 5 is placed a further distance D away from S. (Find the path difference ifz = =>. ia () 22 (©) 32% (i) Find the ratio ofthe maximum to minimum intensity observed on S, if fa) 4 (b) 2 (o) are separated by a small dist @ 1 ‘Two coherent point sources S, and 5. obtained on the screen will be (a) concentric circles ‘ance d as shown in figure. The fringes (b) points as (©) straight lines ic (A) semi-circles Screen7 (iv) In th structive interferen he case of light w «will be COP ‘aves Irom two coheres ces dd S,, there ¥' n Wo coherent sources $, and Sy arbitrary point p, eee the path ditference $,P— 5,P is (d) A © (n+!) a) pin et : n- 3 ea phase difference of () ‘Iwo Monochrom, dee _ a Matic light waves of amplitudes 34 and 2A interle aL {hat point will be proportional to (by 14 60°. The intensity (a) 542 (d) 19A" Ve The Wavefront Wavetront is Accord he wavefront vendicular to th 7 and the 4 locas of points which vibratic in same phase. A ray of light is perp. rae i f0 Huygens principle, each point of the wavetront is the source of a secondary CS Wavelets connecting trom these points spread out in all directions with the speed! of the figure shows a surface XY separating two transparent media, medium-1 and med f epresent wavefronts of a light wave travelling in medium 1 and incident on XY. the lines ¢/ wavefronts of the light wa wave fium-2. the lines ab and ed and gh represent n medium-2 after refraction. b ‘ wa amd -2 oe (i) Light travels asa (a) parallel beam in each medium (b) convergent beam in each me (©) divergent beam in each medium m and convergent beam in the other medium, (d) divergent beam in one medi (ii) ‘The phases of the light wave at c, d,¢ and fare 0,, 64,9, and 9, respectively. It is given that 9, + 9, (a) 9, cannot be equal to oy (b) 9, can be equal to 9, (6) (oy opis equal to (0, = 0) (a) (04 8) is not equal to (9,~ 0.) (iii) Wavefront is the locus of all points, where the particles of the medium vibrate with the same (a) phase (b) amplitude (0) frequency (d) period (iv) A point source that emits waves uniformly in all directions, produces wavefronts that are (a) spherical (b) elliptical (©) cylindrical (d)_ planar (v) What are the types of wavefronts ? (a) Spherical (b) Cylindrical (©) Plane ao Huygens Principle Huygen’s principle is the basis of wave theory of light, Each point on a wavettont acts as a fre: disturbance, called secondary waves or wavelets. ‘The secondary wavelets spread out in all di speed light in the given medium, all di 'sh source of new rections with theSO —— initially parallel cylindrical beam trav f positive constants and [1c radius, isthe intensity of the lig ) of refractive index j({) = thy + yh where Hy and M. The intensity of the beam is decreasing with incre (i) The initial shape of the wavefront of the beam is (a) planar (b) convex (©) concave (d) convex near the axis and concave near the periphery (ii) According to Huygens Principle, the surface of constant phase is (a) called an optical ray (b) called a wave (6) called a wavefront (d) always linear in shape As the beam enters the medium, it will (a) travel as a cylindrical beam (b) diverge (©) converge (d) diverge near the axis and converge near the periphery. ix) Two plane wavefronts of light, one incident on a thin convex lens and another on the refracting face of a thin prism. After refraction at them, the emerging wavefronts respectively become (a) plane wavefront and plane wavefront (b) plane wavefront and spherical wavefront (c)_ spherical wavefront and plane wavefront (d) spherical wavefront and spherical wavefront (v) Which of the following phenomena support the wave theory of light? 1. Scattering 2. Interference 3. Diffraction 4. Velocity of light in a denser medium is less than the velocity of light in the rarer medium | | (a) 12,3 (b) 1,24 (©) 2,34 @ 134 Diffraction of Light ‘The phenomenon of bending of light around the sharp corners and the 5} t| e spreading of il shadow of the opaque obstacles is called diffraction of light. ‘The light thus rich eta ain deviation becomes much more pronounced, when the dimensions of the aperture or the obaincia ne ete to the wavelength of light. or the obstacle are comparableed Incident Dilfracte cer | pt Ir i. é — be (Light seems to propagate in rectilinear path because (2) its spread ss very large (b) its wavelength is very small (c)_ reflected from the upper surface of atmosphere (© itis not absorbed by atmosphere (Gi) In ditfraction from a single sit the angular width of the central maxima does not depends on (a) Aoflight used (b) width of slit (©) distance of slits from the screen (d) ratio of 4. and slit width (ii) For a ditfraction from a single slit, the intensity of the central point is, (a) infinite (b) finite and same magnitude as the surrounding maxima (©) finite but much larger than the surrounding maxima (d) finite and substantially smaller than the surrounding maxima ) Resolving power of telescope increases when (a) wavelength of light decreases (b) wavelength of light increases (© focal length of eye-piece increases (a) focal length of eye-piece decreases (¥)_ Ina single diffraction pattern observed on a screen placed at D metre distance from the slit of width d metre, the ratio of the width of the central maxima to the width of other secondary maxima is (a) 2:1 (b) 1:2 (ant (a) 3.1 Interference of Light Waves and Young's Experiment Interference is based on the superposition principle. According to this principle, at a particular point in the medium, the resultant displacement produced by a number of waves is the vector sum of the displacements produced by each of the waves. If two sodium lamps illuminate two pinholes S, and S,, the intensities will add up and no interference will be observed on the screen. Here the source undergoes abrupt phase change in times of the order of 10"! seconds, fringes Sedum Lamp | | is ant Sodiurn Lain S: Seren, SA a A CeSF of 5. Find the ratio ‘maximum intensity to my se Asiluealcaectalystsnie- teas (@) 1554 (b) 16.78, (co) 19.72 ne (iD Which of the Jollowing ; (a) s ‘ap bubble Hoes not show inter 2 show interference (dy Wedge shaped film spacing on (D)_ Excessively thin fil » (co) Athick film (iii) In a Young’s dou 1 the same fringe teste the screen, the ser . reen-to-slit distance D must be changed te (@) 2p () aD Dv) (a) pit (1) The maximum number of possible interference maxima for sit separation equal fo twice the wavelength H Young's double-stit experiment, is (a) infinite (b) tive (0) three (oa (9) The resultant amplitude of a vibrating particle by the superposition of the two waves v= asinfor+ "Jandy, = | fand yy =a sin en is (ly via (a) a (b) V2a (©) 2a ME, Ssention ere so nd the other labelled For question numbers 11-30, two st s are given-one labelled Assertion (A) =e Reason (R). Select the correct answer to these questions from the codes (a), (b), (6) and (a) as piven Delo (a) Both A and R are true and R is the correct explanation of A (b) Both A and R are true but R is NOT the correct explanation of A (©) Aistrue but R is false (d) A is false and R is also fa 11. Assertion (A) : A narrow pulse of ight is sent through a medium. ‘Ihe pulse will retain its shape as if travels through the medium. Reason (R) : A narrow pulse is made of harmonic waves with a large range of wavelengths 12, Assertion (A): When monochromatic light is incident on a surface separating two media, the reflected and refracted light both have the same frequency as the incident frequency. Reason (R): The frequency of monochromatic light depends on media. Assertion (A) : Light added to light can produce darkness, Reason (R) : The destructive interference of two coherent light sources may give dark tringe 14. Assertion (A) : In YDSE bright and dark fringe are equally spaced. Reason (R) : It only depends upon phase difference. 15. Assertion (A) : When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the shadow of the obstacle. Reason (R) : Wave diffracted from the edges of circular obstacle intertere constructively at the centre of the shadow resulting in the formation of bright spot 16. Assertion (A) : Newton’ rings are formed in the reflected system. When the space between the lens and the oe nee is filled with a liquid of refractive index greater than that of glass, the central spot of the pattern 8 dark. Reason (R) * The reflections in Newton’ ring cases will be from a denser to a rarer medium and the two interfering: ays are reflected under similar conditions19, 29. 30. e width, of same tof posi eintet and minima in the Interierenes \ vo slits shoud be edu ; vr saws re of amplitude. portional ence all the fringes af© jon of the fi ndepend pattern of Youngs 4, In interference fringe width is eres Assertion (A) : For best contrast between maxima allt experiment, the intensity of light emerging out of aan ince pattern ts pret iment the 0 tis. Ata point on th ngth of W ed apart. Interference pattern fe at distance eee nen it is directly opposite to portional to square of distance The intensity of interte Assertion (A) : In Youngs double slit expe sobserved on a screen at distance D from th One of the slits, a dark fringe is observed. Then the of two slits Reason (R) : For a dark t eis pr nge intensity is 7010. portional to wavelength of the source Assertion (A) : In Young’ experiment the fringe width is directly Pro used fe sung’ experiment, the Reason (R) : When a thin transparent sheet is place in front of both the slits of Youngs XP fringe width will increase Assertion (A) : Interference obeys the law of conservation of energy. Reason (R) : The energy is redistributed in case of interference. Iine as shown. Pand Qare two Assertion (A) : Two point coherent sources of light S, and S, are placed on & ae Points on that line. Ifat point P maximum intensity is observed then maximum intensity SNe observe ee Po . os se 3 Reason (R) : In the figure of assertion the distance |S, - S,P| is equal to distance |8,Q ~ S,Q| Assertion (A) : We cannot get diffraction pattern from a wide slit illuminated by monochromatic light. Reason (R) : In diffraction pattern, all the bright bands are not of the same intensity Assertion (A) : When a light wave travels from a rarer to a denser medium, it loses speed. The reduction in speed imply a reduction in energy carried by the light wave. Reason (R) : The energy of a wave is proportional to velocity of wave. Assertion (A) : The interference pattern is observed when source is monochromatic and coherent. Reason (R) : In Young's double slit experiment, we observe an interference pattern on the screen if both the slits are illuminated by two bulbs of same power. Assertion (A) : Young's double slit experiment can be performed using a source of white light. Reason (R) : The wavelength of red light is less than the wavelength of other colours in white light Assertion (A) : The film which appears bright in reflected system will appear dark in the transmitted light and vice-versa. Reason (R) : The conditions for film to appear bright or dark in reflected light are just reverse to those in the transmitted light. Assertion (A) : In Young’ double sit experiment, the fringes become indistinct if one of the slits is covered with cellophane paper. Reason (R) : The cellophane paper decrease the wavelength of light. [Assertion (A) : One of the condition for interference is thatthe two source should be very narrow. Reason (R) : One broad source is equal to large number of narrow sources. arch “Assertion (A) : When tiny circular obstacle is placed in the path of light from some distance spot is seen at the centre ofthe shadow of the obstacle, we dstance, a bright Reason (R) : Destructive interference occurs at the centre of the shadow,tringe width is p= 2? a@ “hte Disthe distance ot the slits from the screen, di th 2, the w eDaration Thetetore the either by eh. Nof the slits and tinge width (ean Manging the separ ‘avelength. be changed lion between the sources Ne Sources OF the distance of th trom th We screen from the GDC): ASthe wi alth of one of the s elaan he slits is increased to Hitude due to slit become 2a GHD (A): Ae = Cy — NE Cy — tg Hala Bate U4 t= t= ty WAX > 0, then fringe pattern will shitt upward. WAX <0, then fringe pattern will shift downwards. iv) (b): Contra will be reduced. between the bright and dark fringes () (a): Sines of the slit is covered, interference will not occur and fringe pattern will disappear, 2 Gi maxima on the screen is, dsin = m2 1d is the wavelength. n@= nh or 2sind =n (b):The condition for possible interference where d is slit separation As d= 2, (given) For number of interference maxima to be maximum, sind n=2 The interference maxima will be formed when n=0, £1, 42 Hence the maximum number of possible maxima is 5 aD (ii) (©): Fringe width, B= [> “s. If we replace yellow light with blue light, ic. Jonger wavelength with shorter one, therefore the fringe width decreases. d , (iii) (@): d’ = 5 and D aD Fringe width, B = 7 (in)-# (iv) (When Youngs double slit experiment ‘New fringe width B’ is repeated in water, instead of ate A= yr uD tinge width wavelength, decteases. B= Ape + be HMB decreases, . The tringe become narrower e fringe at the Jt, we get white Fringe a central maximum, Wh ot changed (¥) (a): Using white Ii centre ie, white fringe is the the sereen is moved, its position &s osm 3.) (eo llere, d= 0.1 mm, 2, = 000 AvP O° For third dark band, dsin® = 3% + sin® => 3h _3x05%6x107 yg. 19 'm=9mM yea > o1mio* m 0.2 «10 hm. (ii) (b): Given d = 02 7. = 5000 A= 510 7m The distance between the first of the central maximum 2AD _2x5x10 7X2 ag 2m d 02x10" minimum on other side (iti) (a) Her 600 nm = 6 107m @=0.2mm-=2«10'm.o Angular width of central maxima, 2 _2x6x107 a 2x10 * iv) (d): When red lightisreplacea by blue lig the diffraction pattern bands becomes narrow and crowded together 6x10 * rad by 2) (¥)_(b): To observe diffraction, the size of the obstacle should be of the order of wavelength, 4. (i) (€):The optical path difference at Pis Av=5,P-S,P=dcos® cos 8 e ~ > for small y for smal . oe eos fe where D+ d (ii) (b): For n" maxima, = Aven,di fay 207 ¥ = radius of the 1!" bright =f") (HD (@); At the central maxima, 8 = 0. Av=d= nb dos = n=5=—* 1000 a” osx10 Hence, for the closet second bright fringe, = 998. (iv) (6): Light waves from two coherent sources must have a constant phase difterence, (¥)_ (d): Interference is shown by transverse as well as mechanical waves, 5. (i) (d):Path difference produced is Re RF R=nR For maxima: Ax ni, Thus, the possible values off are 22, AR AR ee (i) @) 2 (ii) (b): Maximum intensity, nar = (+) Here, 1, = (given) Ho xpath difference (iv) (d): Phase difference nh is =60° As Wa 6.a 3, A 6 ? ex cos” 5 or A? ec cos > Now I / 6.) (DASE = 5G Ax dD ad _® ddd 2 2D (i) ()82= 7 aDd _ dd Hence, maxima at S, as well a5 Sy Resultant intensity at Sy, 1= lo (4)? +441)? AUS, + Ax Avat Sy Iya _ (lo) Trin [(4ly)!* -(4lo) (iti) (a): When the screen is Pl to the line joining the sources, centric circles. laced perpendicular the fringes will be co (iv) (b): Constructive interference occurs when the path difference (S,P - SP) isan integral multiple of 7 or $,P=—S;P=mh, where n= 0, 1, 2.3. (W) (@): Here, A, = 3A, A, = 2A and 0 = 60° The resultant amplitude at a pol ‘As, Intensity 2= (Amplitude)? ‘Therefore, intens! Tee 192 i the same point is, 7. (W (a):Since the path difference between two waveform is equal, light traves as parallel beam in each medium. (ii) (©): Since all points on the same phase, y= Qand 9/= 0, 2 Oy 87> 8 = % wavetront are in the r (iid) (a) : Wavefront is the locus of all ints, whe particles of the medium vib Feats where the ate with the same phaseya) «) (d) 8. (i) (a):As the beam is initially parallel, the shape of wavefront is planar. (ii) (c): According to Huygens Principle, the surface of constant phase is called a wavefront. (iii) (©) (iv) (o): After refraction, the emerging wavefronts respectively become spherical wavefront and plane wavefront as shown in figures (a) and (b). Incident plane Spherical Incident plane Plane wavefront wavefront wavefront wavefront w) © 9. (i) (b): The wavelength of visible light is very small, that is hardly shows diffraction, so it seems to propagate in rectilinear path, (ii) (c): Angular width of central maxima, 26 = 2/e. Thus, @ does not depend on screen i¢., distance between the slit and the screen. (iii) (c): The intensity distribution of single slit diffraction pattern is shown in the figure. From the graph it is clear that the intensity owcesity of the central point is finite but much larger than the surrounding maxima. oo : a {iv) (a): Resolving power of telescope = 75> “It increases when wavelength of light decreases and/or objective lens of greater diameter is used. 22Die (v) (a): Width of central maxim; width of other secondary maxima = /.D/e ; Width of central maxima: width of other secondary ‘maxima S27 10. (i) (€):Given 1, = 10 W/m? and I, = 25 W/m” 16 4, =0.63244, (ay +ay)" _ (0.63240 +aP _t9g74 n (a, ay)? (0.63240; —ay]” In an excessively thin film, the thickness of “Thus the path difference between 5 2/2 which produces a (ii) (b) the film is negligible. the reflected rays become minima (iii) (a): Since, B= 2» for d = 2d, Dp, =20 (iv) (b): The condition for possible interference maxima on the screen is, dsin® = 1 ation and 7. is the wavelength. where d is slit separa As d = 22. (given) 2asin6 = ni, or 2sin8 =n For number of interference maxima to be maximum, n=2 sind = 1 ‘The interference maxima will be formed when n=0, +1, +2 Hence the maximum number of possible maxima is 5. () (ds =asin(or +5 Jand yy =asinot A= yap +a} +2aa, coso, where > = JI. (c):A narrow pulse is made of harmonic waves with a large range of wavelengths, As speed of Propagation is different for different wavelengths, the pulse cannot retain its shape while travelling through the medium. 12, (©): The reflection and refraction of light occurs on account of interaction of light with the atoms of the surface of separation. These atoms can be regarded as oscillators, Light incident on the interface forces the atomi oscillators to oscillate with frequency of incident light. As frequency of light emitted by these (charged)cit tons sequal to their ow a ‘qual to their own re Me, retlected and ret ‘quency of oscillation, Hracted light have the same ‘at light frequency as that ot incite 13, (4): When light waves from two coherent N trough of the othor test, the amplitud 14 (6): Fringe width ive by, OR where, D = distance between ali ad, screen #© wavelength of incident ligt ts ofMaine! wh Path difference between the two interfering wavesis an integral length peat 16. (a): The central spot when the medium he plan Newtons Plane conver tens selass 1s rarer than the medium al lets and glass The central spot is dark because the phhse change of is ark 17. (a) Aven theexprooin p= PB wlth Bis sndepenatent ot (p all the Iringes are of sare width, ithon of fringe), hence 18, (b): When intensity of light ¢ slits is equal, the intensity at minima, wo Whe -vie) eh al cof the slit verging, Irom. two 6, of absoute dark. I 19, we Is observed (bd: For hereS,?=DandS,P = vb? + Path difference 20, (¢): Fringe width P= /.D/d shall remain the same fs the waves travel It alr only, aller passing Uxrough the thin transparent sheet. Due to introduction of thin sheet, anly path difference of the wave is changed dlue to which there is shift of position of (ringes only, Dy=l, where Hs tolnact ren a8 BG fi and tis its the! which is ness index of thin she' parol mation pce. int 21. (aystn ease of intertete ts nae = lV : 18 Naan 2AYia Wo : ‘vat hon : j ence bea se gfig)_ ant anton energy Phas, is actually apps yotene atthe ing ergy holds maw ws good in the mete ae of inter her created 1 Interference but is redistributed ensity is observed at then Jat QS, 22, (bye H maximum re 1 ntensity to be also obse for maximum ea mun (where mts and, mast have phase differen an integer) 7), bending eye uae not be detected wil ont upto a certain distance of sereen froma the slit, Hence practically, no diffraction occurs. it hecomes so small th 24. (a): Wher a light wave travel from a rarer to a denser medium # loses spel, but energy cartied by at depend on its speed. Listead, the hoes. depends on the amplitude of wave. The frequency also ain constant (c):Itboth the ditsare illuminated by two bulbs of Me Power, No interference pa von the screen. This iy because waves reaching at any fern will be observed point on the screen do not have a cons phase difference, as phase difference trom two incoherent sources changes randomly. Therofore, maxima and minima would also change their positions randomly and in quick succession. ‘This will re {Hlumination ot the screen, Mt in general 26. (6): When double slit experiment iso! white light, the central fringe is white as all colours meet there in phase source in Young's 27, (1): For rellected system of the Of constructive interference is maxima for transmittes equation 2ut cose = wi film, the maxima 2nteosr = while the “f system of film is given byPere is thickness of the fil fraction. mand ris angle of rel > for maxima in reflected System and transmitted system are just opposite. y 28. (c): When one of slits is covered with cellophane Paper, the intensity of light emerging from the slit is decreased (because this mediu m is translucent). Now the two interfering beam have different intensities or amplitudes. Hence, intensity at minima will not be zero and fringes will become indistinct. valet large 29. (a): As a broad source is equivalent to a larg Number of narrow sources lying side by side. Each set of these sources will produce an interference pattern of its own which will overlap on another to such an extent that all traces of a fringe system bs lost and results in general illumination. Because of this reason, for interference a narrow slit should be used. 30. (c): The waves diffracted from the gaol circular obstacle, placed in the path of light, inte! constructively at the centre of the shadow resulting in the formation of a bright spot.