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1 PLANCESS RANK ACCELERATOR PHYSICS FOR JEE MAIN & ADVANCED Wave Optics 4000+questions with topic wise exercises 000+ problems of IIT-JEE & AIEEE exams of last 5 years 4 Levels of Exercises categorize into JEE Main & Avance 7 Types of Questions base on latest JEE pattern Detaile Solutions of all questions are available PlancEssential Questions recommene for revision

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3 EXERCISE JEE MAIN / BOARDS Q. State the essential conition for iffraction of light to occur. The light of wavelength 600mn is incient normally on a slit of with mm. Calculate the linear with of central maximum on a screen kept m away from the slit. Q. (a) State the postulates of Huygens s wave theory. (b) Draw the type of wave front that correspon to a beam of light (i) coming from a very far-off source an (iii) iverging from a point source. Q. In a single slit iffraction pattern, how oes the angular with of central maximum change, when (i) slit with is ecrease (ii) istance between the slit an screen in increase an (iii) light of smaller visible wavelength is use? Justify your answer in each case. Q.4 Derive Snell s law of refraction using Huygens s wave theory. Fin the ratio of intensities at two points on a screen in Young s ouble slit experiment, when waves from the two slits have path ifference of (i) 0 (ii) 4 Q.8 Two narrow slits are illumination by a single monochromatic source. Name the pattern obtaine on the screen. One of the slits is now completely covere. What is the name of the pattern now obtaine on the screen? Draw intensity pattern obtaine in the two cases. Also write two ifference between the patterns obtaine in the above two cases. Q.9 Using Huygens s Principle, raw a iagram to show propagation of a wave-front originating from a monochromatic point source. Describe iffraction of light ue to a single slit. Explain formation of a pattern of fringes obtaine on the screen an plot showing variation of intensity with angle single slit iffraction. in Q.5 Explain with reason, how the resolving power of a compoun microscope will change when (i) frequency of the incient light on the objective lens in increase, (ii) focal length of the objective lens is increase, an (iii) aperture of the objective lens is increase. Q.6 What is a wavefront? What is the geometrical shape of a wave front of light emerging out of a convex lens, when point source is place at its focus? Using Huygens s principles show that, for a parallel beam incient on a reflecting surface, the angle of reflection is equal to the angle of incience. Q.7 Two slits in Young s ouble slit experiment are illuminate by two ifferent lamps emitting light of the same wavelength. Will you observe the interference pattern? Justify your answer. Q.0 What are coherent sources of light? State two conitions for two light sources to be coherent. Derive a mathematical expression for the with of interference fringes obtaine in Young s ouble slit. Q. Define resolving power of a compoun microscope. How oes the resolving power of a compoun microscope change when (i) refractive inex of the meium between the object an objective lens increases? (ii) wavelength of the raiation use in increase? Q. State one feature by which the phenomenon of interference can be istinguishe from that of iffraction. A parallel beam of light of wavelength 600nm is incient normally on a slit of with a. If the istance 7.

4 between the slits an the screen is 0.8 m an the istance of n orer minimum from the centre of the screen is 9.5 mm. Calculate the with of the slit. Q. How woul the angular separation of interference fringes in Young s ouble slit experiment change when the istance between the slits an screen is ouble? Q.4 Define the term linearly polarize light. When oes the intensity of transmitte light become maximum, when a polaroi sheet is rotate between two crosse polarois? Q.5 In Young s ouble slit experiment, monochromatic light of wave length 60nm illuminates the pair of slits an prouce an interference pattern in which two consecutive bright fringes are separate by 8.mm. Another source of monochromatic light prouces the interference pattern in which the two consecutive bright fringes are separate by 7. mm. Fin the wavelength of light from the secon source. What is the effect on the interference fringes if the monochromatic source is replaces by a source of white light? Q.6 (a) In a single slit iffraction experiment, a slit of with is illuminate by re light of wavelength 650nm. For what value of will (i) the first minimum fall at an angle of iffraction of 0, an (ii) the first maximum fall at an angle of iffraction of 0? (a) Why oes the intensity of the seconary maximum becomes less as compare to the central maximum? Q.7 When light travels from a rarer to a enser meium, the spee ecreases. Does this ecrease in spee imply a ecrease in the energy carrie by the light wave? Justify your answer. Q.8 In Young s ouble slit experiment, the two slits 0. mm apart are illuminate by monochromatic light of wavelength 40 nm. The screen is.0 m away from the slits. (a) Fin the istance of the secon (i) bright fringes, (ii) ark fringes from the central maximum. (b) How will the fringes pattern change if the screen is move away from the slits? Q.9 How oes an unpolarise light get polarize when passes through a polaroi? Two polarois are set in crosse position. A thir Polaroi is place between the two making an angle with the pass axis of the first Polaroi. Write the expression for the intensity of light transmitte from the secon Polaroi. In what orientations will the transmitte intensity be (i) minimum an (ii) maximum? Q.0 How oes the angular separation between fringes in single-slit iffraction experiment change when the istance of separation between the slit an screen is ouble? Q. For the same value of angle of incience, the angle of refraction in three meia A, B an C are 5, 5 an 5 respectively. In which meium woul the velocity of light be minimum? Q. (a) In Young s ouble slit experiment, erive the conition for (i) constructive interference an (ii) estructive interference at a point in the screen. (b) A beam of light consisting of two wavelengths, 800nm an 600nm is use to obtain in the interference fringes in a Young s ouble slit experiment on a screen place.4 m away. If the two slits are separate by 0.8 mm, calculate the least istance from the 7.

5 central bright maximum where the bright fringes of the two wavelengths coincie. Q. (a) How oes an unpolarize light incient on light on polaroi get polarize? Describe briefly, with the help of a necessary iagram, the polarization of light by reflecting from a transparent meium. (b) Two polarois A an B are kept in crosse position. How shoul a thir polaroi C be place between them so that the intensity of polarize light transmitte by polaroi B reuce to /8 th of the intensity of unpolarize light incient on A? Q.4 Two sources of intensity I an unergo interference in Young s ouble slit experiment. Show that I a a I a a max min I Where a an a are the amplitues of isturbance for two sources S an S. Q.5 Two coherent waves of equal amplitue prouce interference pattern in Young s ouble slit experiment. What is the ratio of intensity at a point where phase ifferent is to intensity at centre. 7.

6 EXERCISE JEE MAIN Single Correct Question Q. Two coherent monochromatic light beams of intensities I an 4I are superpose. The maximum an minimum possible intensities in the resulting beam are: (A) 5I an I (B) 5I an I (C) 9I an I (D) 9I an I Q. When light is refracte into a enser meium, (A) its wavelength an frequency both increase (B) its wavelength increase but frequency remains unchange (C) its wavelength ecreases but frequency remain unchange (D) it wavelength an frequency both ecrease. Q. In YDSE how many maxima can be obtaine on the screen if wavelength of light use is 00nm an 700nm: (A) (B) 7 (C) 8 (D) none of these l l n (A) (B) 4 (C) l l n l l l l n 4 l l l l n (D) 4 Q.6 In a young s ouble slit experiment, a small etector measures an intensity of illumination of I units at the centre of the fringe pattern. If one of the two (ientical) slits is now covere, the measure intensity will be (A) I (B) I (C) I/4 (D) I/ Q.7 In a Young s ouble slit experiment D equals the istance of screen an is the separation between the slit. The istance of the nearest point to the central maximum where the intensity is same as that ue to a single slit, is equal to (A) D (B) D (C) D (D) D Q.4 In Young s ouble slit experiment, the wavelength of re light is 7800Å an that of blue is 500 Å. The value of n for which th n bright ban ue to re light coincies with n th bright ban ue to blue light is: (A) (B) (C) (D) 4 Q.8 A plane wavefront AB is incient on a concave mirror as shown. Then, the wavefront just after reflection is Figure 7.9 Q.5 Two ientical narrow slits S an S are illuminate by light of wavelength from a point source P. If, as shown in the iagram above, the light is then allowe to fall on a screen, an if n is a positive integer, the Figure 7.8 conition for estructive interference at Q is () None of the above Q.9 In a Young s ouble slit experiment, first maxima is observe at a fixe point P on the screen. Now the screen is continuously move away from the plane of slits. The ratio of intensity at point P to the intensity at point O (center of the screen) 7.4

7 (C) x (D) x (A) remains constant (B) keeps on ecreasing (C) first ecrease an then increases (D) First ecreases an then becomes constant Q.0 In the figure shown if a parallel beam of while light is incient on the plane of the slits then the istance of the while spot on the screen from O is [Assume <<D <<] (A) 0 (B) / (C) / (D) /6 Q. In Young s ouble slit arrangement, water is fille in the space between screen an slits. Then: (A) fringe pattern shifts upwars but fringes with remain unchange. (B) fringe with ecreases an central bright fringe shift upwars. (C) fringe with increases an central bright fringe oes not shift. (D) fringe with ecreases an central bright fringe oes not shift. Q. Light of wavelength in air enters a meium of refractive inex. Two points in this meium, lying along the path of this light, are at a istance x apart. The phase ifference between these points is: (A) x Figure 7.40 (B) x Figure 7.4 Q. In YDSE, the source place symmetrically with respect to the slit is now move parallel to the plane of the slits so that it is closer to the upper slit, as shown. Then, (A) the fringe with will remain an fringe pattern will shift own (B) the fringe with will remain same but fringe pattern will shift up (C) the fringe with will ecrease an fringe pattern will shift own (D) the fringe with will remain same but fringe pattern will shift own Q.4 In a YDSE with two ientical slits, when the upper slit is covere with a thin, perfectly transparent sheet of mica, the intensity at the centre of screen recs to 75% of the initial value. Secon minima is observe to the above this point an thir maxima below it. Which of the following can not be a possible value of phase ifference cause by the mica sheet. (A) (B) (C) 7 (D) Q.5 Two monochromatic an coherent point sources of light are place at a certain istance from each other in the horizontal plane. The locus of all those points in the horizontal plane which have constructive interference will be: (A) a hyperbola (B) family of hyperbolas (C) family of straight lines (D) family of parabolas Figure 7.4 Q.6 A circular planar wire loop is ippe in a soap solution an after taking it out, hel with 7.5

8 its plane vertical in air. Assuming thickness of film at the top to be very small, as sunlight falls on the soap film, & observer receive reflecte light (A) the top portion appears ark while the first colour to be observe as one moves own is re (B) the top portion appears violet while the first colour to be observe as one moves own is inigo (C) the top portion appears ark while the first colour to be observe as one moves own is violet (D) the top portion appears ark while the first colour to be observe as one moves own is epens on the refractive inex of the soap solution. Q.7 A thin film of thickness t an inex of refraction. coats a glass with inex of refraction.50. What is the least thickness t that will strongly reflect light with wavelength 600nm incient normally? (A) 5nm (B) 00nm (C) 400nm (D) 450nm Q.8 Spherical wave fronts shown in figure, strike a plane mirror. Reflecte wavefronts will be as shown in (B) same amplitue (C) a constant phase ifference (D) the same intensity Q.0 If the source of light use in a Young s Double Slit Experiment is change from re to blue, then (A) the fringes will become brighter (B) consecutive fringes will come closer (C) the number of maxima forme on the screen increases (D) the central bright fringe will become a ark fringe. Q. In a Young s ouble slit experiment, green light is incient on the two slits. The interference pattern is observe on a screen. Which of the following changes woul cause the observe fringes to be more closely space? Figure 7.4 (A) Rcing the separation between the slits (B) Using blue light instea of green light (C) Use re light instea of green light (D) Moving the light source further away from the slits. Multiple Correct Question: Q.9 To observe a sustaine interference pattern forme by two light waves, it is not necessary that they must have: (A) the same frequency Q. In a Young s ouble-slit experiment, let A an B be the two slits. A thin film of thickness t an refractive inex is place in front of A. Let fringe with. The central maximum will shift: (A) towars A (C) by t (B) towars B (D) by t 7.6

9 Q. In the previous question, films of thickness t A an t B an refractive inices A an B, are place in front of A an B respectively. If t A A t B B, the central maximum will: (A) not shift (B) shift towars A (C) shift towars B (D) option (B), if t B t A ; option (C) if t B t A Q.4 To make the central fringe at the centre O, a mica sheet of refractive inex.5 is introuce. Choose the correct statement(s). Figure 7.44 Assertion an Reason: (A) Statement - is true, statement- is true an statement- is correct explanation for statement- (B) Statemen- is true, statement- is true an statement- is NOT the correct explanation for statement- (C) Statemen- is true, statement- is false (D) Statement- is false, statement- is true Q.6 Statemen-: In YDSE, as shown in figure, central bright fringe is forme at O. If a liqui is fille between plane of slits an screen, the central bright fringe is shifte in upwar irection. Statemen-: If path ifference at O increases y- coorinate of central bright fringe will change. (A) The thickness of sheet is in front of S. (B) The thickness of sheet is of S. (C) The thickness of sheet is. in front in front of (D) The thickness of sheet is in front of S. Q.5 In a stanar YDSE apparatus a thin film.5,t.m is place in front of upper slit. How far above or below the centre point of the screen are two nearest maxima locate? Take Dm, mm, 4500Å.(Symbols have usual meaning) (A).5mm (C) 0.5mm (B) 0.6mm (D) 0.mm S Figure 7.45 Q.7 Statemen-: In glass, re light travels faster than blue light. Statemen-: Re light has a wavelength longer than blue. Q.8 Statemen-: In stanar YDSE set up with visible light, the position on screen where phase ifference is zero appears bright Statemen-: In YDSE set up magnitue of electromagnetic fiel at central bright fringe is not varying with time. Comprehension type Question The figure shows a schematic iagram showing the arrangement of Young s Double Slit Experiment: Figure

10 Q.9 Choose the correct statement(s) relate to the wavelength of light use (A) Larger the wavelength of light larger the fringe with (B) The position of central maxima epens on the wavelength of light use (C) If white light is use in YDSE, then the violet forms its first maxima closest to the central maxima (D) The central maxima of all the wavelength coincie Q.0 If the istance D is varie, then choose the correct statement(s) (A) The angular fringe with oes not change (B) The fringe with change in irect proportion (C) The change in fringe with is same for all wavelengths (D) The position of central maxima remains unhange Q. If the istance is varie, then ientify the correct statement (A) The angular with oes not change (B) The fringe with changes in inverse proportion (C) The positions of all maxima change (D) The positions of all minima change 7.8

11 PREVIOUS YEARS QUESTIONS JEE MAIN Q : In Young s ouble slit experiment, the separation between the slits is halve an the istance between the slits an the screen is ouble. The fringe with is (98) (a) unchange (C) ouble (b) halve (D) quaruple Q : Two coherent monochromatic light beams of intensities I an 4I are superimpose. The maximum an minimum possible intensities in the resulting beam are (988) (a) 5I an I (c) 9I an I (b) 5I an I () 9I an I Q 4: In a ouble slit experiment instea of taking slits of equal withs, one slit is mae twice as wie as the other, then in the interference pattern. (000) (a) the intensities of both the maxima an the minima increase (b) the intensity of the maxima increases an the minima has zero (c) the intensity of the maxima ecreases an that minima increases. () the intensity of the maxima ecreases an the minima has zero. Q 5: Two beams of light having intensities I an 4I interfere to prouce a fringe pattern on a screen. The phase ifference between the beams is at point A an at point B. Then the ifference between resultant intensities at A an B is (00) (A) I (B) 4I (C) 5I (D) 7I Q 6: In a YDSE bi-chromatic light of wavelengths 400nm an 560nm is use. The istance between the slits is 0.mm an the istance between the plane of the slits an the screen is m. The minimum istance between two successive regions of complete arkness is (a) 4mm (b) 5.6mm (c) 4mm () 8mm (004) Q 7: In Young s ouble slit experiment intensity at a point is (/4) of the maximum intensity. Angular position of this point is (a) sin (c) sin (b) sin () sin 4 (005) Q 8: A narrow monochromatic beam of light intensity I is incient on a glass plate as shown in figure. Another ientical glass plate is kept close to the first onean parallel to it. Each glass plate reflects 5 per cent of the light incient on it transmits the remaining. Fin the ratio of the minimum an maximum Figure 7.47 intensities in the interference pattern forme by the two beams obtaine after one reflection at each plate. (990) Q 9: Angular with of central maximum in the Fraunhofer iffraction pattern of a slit is measure. The slit is illuminate by light of wavelength 6000 Å. When the slit is illuminate by light of another wavelength, the angular with ecreases by 0%. Calculate the wavelength of this light. The same ecrease in the angular with of central maximum is obtaine when the original apparatus is immerse in a liqui. Fin refractive inex of the liqui. (996) 7.9

12 Q 40: A ouble slit apparatus is immerse in a liqui of refractive inex.. it has slit separation of mm an istance between the plane of slits an screen is.m. The slits are illuminate by a parallel beam of light whose wavelength in air is 600 Å. (996 (a) Calculate the fringes with. (b) One of the slits of the apparatus is covere by a thin glass sheet of refractive inex.5. Fin the smallest thickness of the sheet to bring the ajacent minimum as the axis. Q 4: In a Young s ouble slit experiment, two wavelengths of 500nm an 700nm were use. What is the minimum istance from the central maximum where their maximas coincie again? Take D 0. Symbols have their usual meanings. (004) 7.0

13 EXERCISE JEE ADVANCED Q. Two coherent waves are escribe by the expressions. x E E0sin ft 6 x E E0sin ft 8 Determine the relationship between x an that prouces constructive interference when the two waves are superpose. Q. In a Young s ouble slit experiment for interference of light, the slits are 0. cm apart an are illuminate by yellow light x 600nm. What woul be the fringe with on a screen place m from the plane of slits if the whole system is immerse in water of inex 4/? Q. In young s ouble slit experiment the slits are 0.5 mm apart an the interference is observe on a screen at a istance of 00cm from the slit. It is foun that the 9 th bright fringe is at a istance of 7.5mm from the secon ark fringe from the centre of the fringe pattern on same sie. Fin the wavelength of the light use. Q.4 Light of wavelength 50nm passing through a ouble slit, prouce interference pattern of relative intensity versus eflection angle as shown in the figure. Fin the separation between the slits. istance between two points on the screen having 75% intensity of the maximum intensity. Q.6 The istance between two slits is a YDSE apparatus is mm. The istance of the screen from the slits is m. Microwaves of wavelength mm are incient on the plane of the slits normally. Fin the istance of the first maxima on the screen from the central maxima. Also fin the total number of maxima on the screen. Q.7 One slit of a ouble slit experiment is covere by a thin glass plate of refractive inex.4 an the other by a thin glass plate of refractive inex.7. The point on the screen, where central bright fringe was forme before the introuction of the glass sheets, is now occupie by the 5 th bright fringe. Assuming that both the glass plates have same thickness an wavelength of light use is 4800Å, fin their thickness. Q.8 A monochromatic light of 5000Å is incient on two slits separate by a istance of 50 4 m. The interference pattern is seen on a screen place at a istance of m from the slits. 6 A thin glass plate of thickness.50 m & refractive inex.5 is place between one of the slits & the screen. Fin the intensity at the centre of the screen, if the intensity there is I 0 in the absence of the plate. Also fin the internal shift of the central maximum. Figure 7.48 Q.5 In a YDSE apparatus, mm, 600nm an Dm. The slits iniviually prouce same intensity on the screen. Fin the minimum Q.9 One raio transmitter A operating at 60.0 MHz is 0.0 m from another similar transmitter B that is 80 out of the phase with transmitter. A. How far must an observe move from transmitter A towar transmitter B along the line connecting A an B to reach the nearest point where the two beams are in phase? 7.

14 Q.0 Two microwaves coherent point sources emitting waves of wavelength are place at 5 istance apart. The interference is being observe on a flat non-reflecting surface along a line passing through one source, in a irection perpenicular to the line joining the two sources (refer figure). Consiering as 4mm, calculate the position of maxima an raw shape of interference pattern. Take initial phase ifference Figure 7.49 between the two sources to be zero. Q. Two raio antennas raiating wave in phase are locate at points A an B, 00m apart (Figure). The raio waves have a frequency of 5.80MHz. A raio receiver is move out from point B along a line perpenicular to the line connecting A an B (line BC shown in figure). At what istance from B will Figure 7.50 there be estructive interference? Q. A ray of light of intensity I is incient on a parallel glass-slab at a point A as shown in figure. It unergoes partial reflection an refraction. At each reflection 0% of incient energy is reflecte. The rays AB an unergo interference. the ratio max A B I I. min Fin Figure 7.5 [Neglect the absorption of light] Q. If the slits of the ouble slit were move symmetrically apart with relative velocity v, calculate the number of fringes passing per unit time at a istance x from the centre of the fringes system forme on a screen y istance away from the ouble slits if wavelength of light is. Assume y>> & >>. Q.4 A thin glass plate of thickness t an refractive inex is inserte between screen & one of the slits in a Young s experiment. If the intensity at the centre of the screen is I, what was the intensity at the same point prior to the introuction of the sheet? Q.5 In Young s experiment, the source is re 7 light of wavelength 70 m. When a thin glass plate of refractive inex.5 at this wavelength is put in the path of one of the interfering beams, the central bright fringe shifts by 0 m to the position previously occupie by the 5 th bright fringe. Fin the thickness of the plate. When the source is now 7 change to green light of wavelength 50 m, the central fringe shift to a position initially occupie by the 6 th bright fringe ue to re light without the plate. Fin the refractive inex of glass for the green light. Also estimate the change in fringe with ue to the change in wavelength. Q.6 In a Young s experiment, the upper slit is covere by a thin glass plate of refractive inex.4 while the lower slit is covere by another glass plate having the same thickness as the first one but having refractive inex.7. Interference pattern is observe using light of wavelength 5400 Å. It is foun that the point P on the screen where the central maximum (n0) fell before the glass plates were inserte now has ¾ the original intensity. It is further observe that what use to be the 5 th maximum earlier, lies below (Absorption of light by glass plate may be neglecte). 7.

15 Q.7 A screen is at a istance D80cm from a iaphragm having two narrow slits S is an S which are mm apart. Slit S is covere by a transparent sheet of thickness.5 m t.5 an m t S by another sheet of thickness as shown in figure. Both sheets are mae of same material having refractive inex.40. Water is fille in space between iaphragm an screen. A monochromatic light beam of wavelength is incient normally on the iaphragm. Assuming intensity of beam to be uniform an slits of equal with, calculate ratio of intensity at C to maximum intensity of interference pattern obtaine on the screen, where C is foot of perpenicular bisector of S S. (Refractive inex of water, 4/) 5000 Å Q.8 In the figure shown S is a monochromatic point source emitting light of wavelength500nm. A thin lens of circular shape an focal length 0.0 m is cut into ientical halves L an w L by a plane passing through a iameter. The two halves are place symmetrically about the central axis SO with a gap of 0.5 mm. The istance along the axis from the S to an SO. L L an L is 0.5m, while that from to O is.0m. The screen at O is normal (i) If the thir intensity maximum occurs at the point A on the screen, fin the istance OA. (ii) If the gap between L & L is reuce from its original value of 0.5 mm, will the istance OA increase, ecrease or remain the same? Figure 7.5 Figure 7.5 L Q.9 A coherent parallel beam of microwave of wavelength ouble slit apparatus. The separation between the slits is.0 mm. The intensity of microwaves in measure on screen place parallel to the plane of the slits at a istance of.0m from it, as shown in the figure. (a) If the incient beam falls normally on the ouble slit apparatus, fin the y-coorinates of all the interference minima on the screen. (b) if the incient beam makes an angle of 0 with the x-axis (as in the otte arrow shown in the figure), fin the y- coorinates of the first minima on either sie of the Figure 7.54 central maximum. 0.5 mm falls on a Young s Q.0 In a YDSE with visible monochromatic light two thin transparent sheets are use in front of the slits S an S with.6 an.4 respectively. If both sheets have thickness t, the central maximum is observe at a istance of 5mm from centre O. Now the sheets are replace by two sheets of same material refractive inex but having thickness & t t t t such that t. Now central maximum is observe at istance of 8mm from centre O on the same sie as before. Fin the thickness Dm]. t (in Figure 7.55 m ) [Given: mm. 7.

16 EXERCISE JEE ADVANCED Q. Figure shows plane waves refracte from air to water using Huygens s principle a, b, c,, e are lengths on the iagram. The refractive inex of water w.r.t. air is the ratio: (A) a/e (B) b/e (C) b/ (D) /b () If 4., there will be a total of 8 minima on y axis. () If 7, O will be a maxima. (4) If, there will be only one maxima on the screen. Figure 7.57 Which is the set of correct statement (A),, & (B), & 4 (C),, & 4 (D), & 4 Q. In a YDSE, the central bright fringe can be ientifie: (A) as it has greater intensity than the other bright fringes. (B) as it is wier than the other bright fringes. (C) as it is narrower than the other bright fringes. (D) by using white light instea of single wavelength light. Q. In Young s ouble slit experiment, the two slits act as coherent sources of equal amplitue A an wavelength Figure In another experiment with the same setup the two slits are sources of equal amplitue A an wavelength but are incoherent. The ratio of the average intensity of light at the mipoint of the screen in the first case to that in the secon case is (A) : (B) : (C) 4: (D) none of these Q.4 Two point monochromatic an coherent sources of light wavelength are place on the otte line in front of a large screen. The source emit waves in phase with each other. The istance between S an S is while their istance from the screen is much larger. Then, () If 7, O will be a minima Q.5 Two slits are separate by 0. mm. A beam of 500nm light strikes the slits proucing an interference pattern. The number of maxima observe in the angular range- 0 < < 0 (A) 00 (B) 50 (C) 599 (D) 60. Q.6 In the above question of the light incient is monochromatic an point O is a maxima, then the wavelength of the light incient cannot be (A) (C) D (B) D (D) 6D 8D Q.7 In the figure shown in YDSE, a parallel beam of light is incient on the slit from a meium of refractive inexn. The wavelength of light in this meium is thickness t an refractive inex n is put infront of one slit. The meium between the screen an the plane of the Figure A transparent slab of Figure

17 slits is n. The phase ifference between the light waves reaching point O (symmetrical, relative to the slits) is: n (A) (C) n n n n n t n n t (B) t n (D) n n n t Q.8 In A YDSE experiment if a slab whose refractive inex can be varie is place in front of one of the slits then the variation of resultant intensity at mi-point of screen with ' ' will be best represente by. [Assumes slits of equal with an there is no absorption by slab] Q.9 In the YDSE shown the two slits are covere with thin sheets having thickness t & t an refractive inex an. Fin the position (y) of central maxima (A) Zero (B) td (C) td Multiple Correct Question (D) None Q.0 In a YDSE apparatus, if we use white light then: (A) the fringe next to the central will be re (B) the central fringe will be white Figure 7.60 (C) the fringe next to the central will be violet (D) there will not be a completely ark fringe. Q. If one of the slits of a stanar YDSE apparatus is covere by a thin parallel sie glass slab so that it transmit only one half of the light intensity of the other, then: (A) the fringe pattern will get shifte towars the covere slit (B) the fringe pattern will get shifte away from the covere slit (C) the bright fringes will be less bright an the ark ones will be more bright (D) the fringe with will remain unchange. Q. In an interference arrangement similar to Young s ouble-slit experiment, the slits S & S are illuminate with coherent microwave sources, each of frequency 6 0 Hz. The sources are synchronize to have zero phase ifference. The slits are separate by a istance 50.0m. The intensity I( ) is measure as a function of at a large istance from S & S, where efine as shown if then I( I 0 ) for 0 90 is given by: I I for 0 (A) 0 I I for 90 4 (B) 0 (C) I I0 for 0 is is the maximum intensity (D) I is constant for all values of Figure

18 PREVIOUS YEARS QUESTIONS JEE ADVANCED Q : A narrow slit of with mm is illuminate by monochromatic light of wavelength 600nm. (c) () The istance between the first minima on either sie of a screen at a istance of m is. (994) (a). cm (b).mm (c).4 cm ().4mm Q 4: A parallel monochromatic beam of light is incient normally on a narrow slit. A iffraction pattern is forme on a screen place perpenicular to the irection of the incient beam. At the first minimum of the iffraction pattern, the phase ifference between the rays coming from the two eges of the slit is (998) (a) zero (b) (c) () Q 5: In a Young s ouble slit experiment, fringes are observe to be forme in a certain segment of the screen when light of wavelength 600nm is use. If the wavelength of light is change to 400nm, number of fringes observe in the same segment of the screen is given by (00) (a) (b) 8 (c) 4 () 0 f c is equal to is not equal to c e f Q 8: Shows four situations of stanar Young s oubles slit arrangement with the screen place away from the slits S an S. In each of these S P S P,S P S P an 4 cases 0 0 S P S P, where e is the wavelength of the light use. In the cases B, C an D, a transparent sheet of refractive inex thickness t is paste on slit S an. The thickness of the sheets are ifferent in ifferent cases. The phase ifference between the light waves reaching a point P on the screen from the two P slits is onate by an the intensity by I (P). Match each situation given in Column I with the statement(s) in Column II vali that situation. Column I Column II (A) (p) (P 0 ) 0 (009) Q6: In the ieal ouble-slit experiment, when a glass-plate (refractive inex.5) of thickness t is introuce in the path of one of the interfering beams (wavelength ), the intensity at the position where the central maximum occurre previously remain unchange. The minimum thickness of the glass-plate is (00) (a) (b) (c) () (B) t 4 (c) t () t 4 (q) (P ) 0 (r) I(P ) 0 (s) I(P 0) I(P ) (t) I(P ) I(P ) Q 7: The phases of the light wave at c,, e an f are c,, e an f respectively. It is given that (007) c f (a) c cannot be equal to (b) cannot be equal to e Q 9: In the Young s ouble slit experiment, the interference pattern is foun to have an intensity ratio between the bright an ark fringes as 9. This implies that (98) (a) the intensities at the screen ue to the two slits are 5 units an 4 units respectively. 7.6

19 (b) the intensities at the screen ue to the two slits are 4 units an unit respectively (c) the amplitue ratio is () the amplitue ratio is from C is of intensity 0 intensity at P on the screen. Wm. Calculate Q 0: White light is use to illuminate the two slits in a Young s ouble slit experiment. The separation between the slits is b an the screen is at a istance (>>b) from the slits. At a point on the screen irectly in front of one of the slits, certain wavelengths are missing. Some of these missing wavelengths are (a) (c) b b (b) () b b Q : In an interference arrangement similar to Young s ouble-slit experiment, the slits S an S are illuminate with coherent microwave sources, each of frequency 6 0 Hz. The sources are synchronize to have zero phase ifference. The slits are separate by a istance 50.0m. The intensity I ( ) is measure as a function of where is efine as shown. If maximum intensity then I I 0 is the ( ) for 0 90 is given by (995) (a) I ( ) I 0 for 0 Q : In a moifie Young s ouble slit experiment, a monochromatic uniform an parallel beam of light of wavelength 6000 Å 0 an intensity Figure 7.6 Wm is incient normally on two apertures A an B of raii 0.00 m an 0.00 m respectively. A perfectly transparent film of thickness 000 Å an refractive inex.5 for the wavelength of 6000 Å is place in front of aperture A (see figure). Calculate the power (in W) receive at the focal spot F of the lens. The lens is symmetrically place with respect to the apertures. Assume that 0% of the power receive by each aperture goes in the original irection an is brought to the focal spot. (989) (b) I ( ) I 0 4for 90 (c) I ( ) I 0 for 0 () I ( ) is constant for all values of Figure 7.6 Q : Screen S is illuminate by two point sources A an B. Another source C sens a parallel beam of light towars point P on the screen (see figure). Line AP is normal to the screen an the lines AP, BP an CP are in one plane. The raiant powers of sources A an B are 90 W an 80 W respectively. The beam Figure 7.64 Q 4: In Young s experiment, the source is re 7 light of wavelength 70 m. When a thin glass plate of refractive inex.5 at this wavelength is put in the path of one of the interfering beams, the central bright fringe shift by 0 m to the position previously occupie by the 5 th bright fringe. Fin the thickness of the plate. When the sources is now change to 7 green light of wavelength 50 m, the central 7.7

20 fringe shifts to a position initially occupie by the 6 th bright fringe ue to re light. Fin the refractive inex of glass for green light. Also estimate the change in fringe with ue to change in wavelength. (997) Q 5: In a Young s experiment, the upper slit is covere by a thin glass plate of refractive inex.4 while the lower slit is covere by another glass plate, having the same thickness as the first one but having refractive inex.7. Interference pattern is observe using light of wavelength 5400 Å. It is foun that the point P on the screen, where the central maximum (n0) fall before the glass plates were inserte, now has ¾ the original intensity. It is further observe that what use to be the fifth maximum earlier lies below the point P while the sixth minima lies above P. Calculate the thickness of glass plate. (Absorption of light by glass plate may be neglecte). (997) 7.8

21 PLANCESSENTIAL QUESTIONS EXERCISE JEE MAIN/BOARDS Q. Q.5 Q.6 Q.8 Q. Q. EXERCISE JEE MAIN Q.4 Q.5 Q.8 Q. Q.5 Q.6 Q.8 Q.9 Q.40 EXERCISE JEE ADVANCED Q. Q. Q.8 Q. Q.5 EXERCISE JEE ADVANCED Q.4 Q.7 Q.5 Q. 7.9

22 ANSWER KEY EXERCISE JEE MAIN /BOARDS Q..0 Q. (i) angular with increases (ii) no change (iii) angular with increases Q.5 (i) resolving power increases (ii) remains unchange (iii) resolving power increases Q.7 No, Ratio: Q.9 Intensity becomes 4 Q mm I 0 4 Q. Fringe with becomes twice Q.5 560nm, when the monochromatic source is replace by a source of white light; the fringe with woul change. Q.6 (a) (i) 00nm; (ii) 950nm (b) Intensity of seconary maximum is lesser as compare to central maxima Q.7 No, Energy carrie by a wave epens on the amplitue of the wave, not on the spee of wave propagation. Q.8 (a) (i) 0.007m, (ii) m (b) If screen is move away from the slits fringe pattern will shrink. Q.5 EXERCISE JEE MAIN Q. C Q.6 C Q. D Q.6 C Q. B Q.6 D Q. B, D Q. C Q.7 C Q. A Q.7 A Q. A, C Q.7 A Q. B Q.8 C Q. D Q.8 C Q. D Q.8 C Q.4 B Q.9 C Q.4 A Q.9 B, D Q.4 A Q.9 A, C, D Q.5 D Q.0 D Q.5 B Q.0 B, C Q.5 C, D Q.0 A, B, D PREVIOUS YEARS QUESTIONS JEE MAIN. D. C 4. A 5. B 6. D 7. C a) 400 Angstrom, b) a) 0.6mm, b) mm m EXERCISE JEE ADVANCED Q. n x x 48 Q. 0.5mm Q Å Q mm Q.5 0. mm Q cm app., 5 Q.7 8 m Q.8 0,.5mm Q.9.5m Q.0 48,, 9,,0 m.m Figure

23 Q. 760m,.8m, 89.4m, 9.6m Q. 8: Q. x v y Q.4 Q.5 7 I Isec 0 m,.6, t m (ecrease) Q.6 9. Q.7 /4 m Q.8 (i) mm (ii) increase Q.9 (a) (b) Q.0 no shift, 4 5 EXERCISE JEE ADVANCED Q. C Q. D Q. B Q.4 C Q.5 C Q.6 A Q.7 A Q.8 C Q.9 B Q.0 B, C, D Q. A, C, D Q. A, C PREVIOUS YEARS QUESTIONS JEE ADVANCED. D 4. D 5. B 6. A 7. C 8. A-P, S; B-Q, T; C-T 9. B, D 0. A, C. A, C..97. Wm 6 70 W 6 4. (a) m; b).6; c) m m 7.

24 SOLUTIONS EXERCISE JEE MAIN Sol. Size of obstacle must be comparable to wavelength of light with D m. 0 may be regare as a seconary source of spherical wave, which themselves progress with the spee of light in the meium & whose envelope at later times constitutes the new wave front. Sol. Wave front is the locus of all particles of the meium which vibrate in same phase an where isturbances reach at the same point of time. Consier all the point on a primary wave front to be sources of light, which emit isturbances known as seconary isturbances. Tangent envelope to all seconary wavelets gives the position of new wave front. (i) DM Vtt Vt n i DM DG nt ni sint n sin t i DG Vi i F D M G t (ii) Sol.5 R. P. D. (i) If f increases, ecreases R. P. increases (ii) R. P. oesn t epen on f. (iii) If D increases, R. P increases Sol.6 Wave front is the locus of points having the same phase (a line or a curve, etc) Sol. (i) If ecrease, increases (ii) oesn t epen on D (iii) If ecreases, ecreases Sol.4 Accoring to Huygens theory each point on the leaing surface of a wave isturbance Sol.7 If the wavelength of both the sources is same, then interference may not be possible as even phase ifference must be constant I I + I + II cos (i) 0; I 4I0; I (ii) 90 I ; I I0 Sol.8 With slits interference pattern S 7.

25 With slit iffraction pattern In first case, the maximum intensity is constant as we go from centre. In secon case, the intensities at maximum ecrease as we go from centre. In first case, the fringe length is fixe. In secon case, the fringe angle is fixe. Sol.9 In iffraction pattern Sol.0 Two sources are sai to be coherent if their frequencies are equal an they have a constant phase ifference. Two inepenent sources of light cannot be coherent SP SP x n D x n D P x n If x n n D we will observe maximum intensity If x n (n + ) we will observe minimum intensity. Sol. Resolving power of an instrument is its capacity to resolve points which are close together (i) It oesn t epen on μ of the meium (ii) It s inversely proportional to of light. Sol. In interference, the fringe length remains nearly constant. for minima (m ) & m Only is variable Sol. Angular separation of interference fringes in YDSE epens only on, but not on D. Sol.4 Linearly polarise light is light in which all the electric fiel of all the photons are confine to irection perpenicular to irection of wave. I I0cos I cos 80 D Sol.5 If white light is use, there will no complete arkness as all colours will not be out of phase at a single point centre will be brightest as all colours will be in phase at that point. Sol.6 First maxima First minima Sol.7 hc E h. c value ecrease & also ecreases maintaining the frequency constant. So E is constant. S 7.

26 Sol.8 D (a) (i) n bright : y (ii) st ark : y (b) If D increases ecreases, so fringe with increases. Sol.9 The centre reflects the components perpenicular to the irection I I0 cos Sol.0 In single slit iffraction angular fringe with epens only of, but not on D. Sol. (a) The transparent meium allows components of E only in irection & reflects all its perpenicular components. (b) As A & B are crosse, I0 & I 0 cos I 0 8 I 0 Sol.4 Imin I + I + II.cos & I a Imax a a aa () (a + a) Imin a a a a ( ) (a a ) Sol.5 I0 4I Sol. i I' 0 I + I + Icos90 I I 0 r C sin i sin r C 0 as C C sin r. minimum for r 5. Sol. (a) sin n(for constructive) sin n (for estructive) sin (b) D m 4 mm D 60.4 mm r bright of st light 4 th bright of n light S 7.

27 EXERCISE JEE MAIN + I + I I cos Imax cos I 9I Imin cos Sol. I I for Sol.8 D Imin I So will become Sol. c In enser meium, c ecreases but frequency remains the same. also ecreases. Maximum path ifference 00 nm.5 So, we can get p of,,.,. i.e. 7 maxima. ( n ) D n D Sol.4 n(00) (n + )(500) n (n + ) n Sol.5 ( + ) ( + 4) path by path by S S ( n ) Sol.6 Let intensity ue to single slit by I. By two slits we get I. I I+I+ I I cos() an 0º at centre. I 4I I I 4 Sol.7 Let I be intensity ue to single slit. I I + I + I. I cos I cos I 0º Phase ifference Sol.9 as D increases O I P D I moves away from O. I first ecreases, then increases. Sol.0 /7 / OI 6 So 6 nd D 6nD is not possible. / I O D Sol. as c ecreases, also ecreases so ecreases but there won't be any shift. Sol. µx x µ D for S 7.4

28 phase ifference Sol. S S S µx O O µx t nm Sol.8 Image will coincie with S but on opposite sie. S I Fringe with will not change it epens only on,, D. To get P 0, SO > SO. So O will be below O pattern will shift ownwars. Sol.9 They must have same frequency an constant. They nee not have same AI. Sol.4 Imax 4I0 75% of Imax I0 I0 I0 + I0 + I0.cos cos n ± 60º It's between 6 n minima r maxima only Sol.5 is not possible in the options S S SP SP n Family of hyperbolas with n as variable. Sol.6 First coloure to be receive is violet. As frequency of violet is high, re is high an µre > µviolet Sol.7. t Sol.0 re > blue re > blue Fringe length ecreases. So, no. of maxima increases. Sol. They will get closer, if we use light of lower. i.e. using blue light. If '' ecreases, increases oesn't epen on istance between source an slits. Sol. Central maxima will shift towars A as (µ )t is ae before A. x (µ )t (µ ) t y. B A Sol. P µata + tb P ta + µbtb P ta.tb If ta > tb towars B [same as in previous question] If tb < ta towars A Sol.4 If we put mica sheet in front of S. ( ) (µ )t S 7.5

29 t ( ) In front of S ( ) + (µ )t n. Sol.5 D D m. P (µ )t so P D, 7 7 D m Position of central maxima oesn't change. Rest all maxima, minima positions change. Sol.6 Statement-I is false as path ifference will be zero. µso P S P S P 0 µso Sol.7 ν c ; re > blue An µre > µblue So, light spee of re > light spee of blue. Sol.8 Electromagnetic fiel at a point epens also on time. It's magnitue epens with time So statement-ii is false. Sol.9 D So Central maxima is always at O in this case. violet < re, violet is minimum in visible region. So, violet maxima is closest. Sol.0 D Angular fringe with oesn t epen on D. Central fringe oesn't change from O. Sol. x angular fringe with epens on S 7.6

30 PREVIOUS YEARS QUESTIONS JEE MAIN D Sol. is halve an D is ouble Fringe with will become four times. Correct option is (). Sol. Imax ( I + I ) ( Imin ( I I ) ( Correct option is (c). 4I 4I Sol.4 In interference we know that Imax ( I + I ) an Imin ( I I + ) I ~ I I ) 9I Uner normal conitions (when the withs of both the slits are equal) I I I (say) Imax 4I an Imin 0 When the with of one of the slits is increase. Intensity ue to that slit woul increase, while that of the other will remain same. So, let : I I an I I ( > ) Then, Imax I ( + An Imin I ( ) > 4I ) > 0 Intensity of both maxima an minima is increase. Sol.5 I() I + I + I I cos (i) Here, I I an I 4I At point A, IA I + 4I 5I At point B, IB I + 4I 4I I IA IB 4I Note: Equation (i) for resultant intensity can be applie only when the sources are coherent. In the question it is given that the rays interfere. Interference takes place only when the sources are coherent. That is why we applie equation number (i). When the sources are incoherent, the resultant intensity is given by I I + I ) i.e., 4 th minima of 400 nm coincies with r minima of 560 nm. Location of this minima is, 6 ( 4 )(000)(400 0 ) Y 4 mm 0. Next th minima of 400 nm will coincie with 8 th minima of 560 nm. Location of this minima is, 6 ()(000)(400 0 ) Y 4 mm 0. Require istance Y Y 8 mm Hence, the correct option is (). Sol 7. I Imax I max 4 cos or Imax cos cos x where x sin Substituting in Eq. (i), we get sin or sin Correct answer is (c) Sol 8. Eeach plate reflects 5% an transmits 75%. Incient beam has an intensity I. This beam unergoes multiple reflections an refractions. The corresponing intensity after each reflection an refraction (transmission) are shown in figure. Sol 6. Let nth minima of 400 nm coincies with mth minima of 560 nm, then 400 (n ) (m ) 560 or n m (incient beam) S 7.7

31 Interference pattern is to take place between rays an. I I/4 an I 9I/64 I I min max I I I I 49 Sol 9 Given 6000 Å Let b be the with of slit an D the istance between screen an slit. First minima First minima is obtaine at b sin orb as sin or b Angular with of first maxima b Angular with will ecrease by 0% when is also ecrease by 0%. Therefore, new wavelength 0 ' (6000) 6000 Å 00 ' 400 Å (b) When the apparatus is immerse in a liqui of refractive inex, the wavelength is ecrease times. Therefore, 400 Å 6000Å D or.49.4 Sol 40. Given,., mm, D. m, 600 Å (a) Wavelength of light in the given liqui: ' 600. Å 477 Å m Fringe with, 'D 0 (477 0 m)(.m) m ( 0 m) 0.6 mm (b) Let t be the thickness of the glass slab Path ifference ue to glass slab at centre O..5. glass x t t liqui or x 0.5t Now, for the intensity to be minimum at O, this path ifference shoul be equal to x ' or 0.5 t 477 Å t 5790 Å or t.579 m ' Sol 4. Let n bright fringe corresponing to wavelength 500 nm coincies with n bright fringe corresponing to wavelength 700 nm. D D n n or n n 7 5 O This implies that 7 th maxima of coincies with 5 th maxima of. Similarly 4 th maxima of will coincie with 0 th maxima of an so an. nd Minimum istance m.5 mm S 7.8

32 EXERCISE JEE ADVANCED Sol. For constructing interference x (x x ) n 8 6 (x x) Sol. D n 48 ; m. 4 0 Sol. 9 th Bright fringe n ark fringe D 4 9D (9 -. 5) m 5000 Å. Sol.4 P sin sin mm Sol.5 Imax 4I0 75% of Imax I0 I0 I0 + I0 + I0I0 cos cos 60, 60 0 D 60 D 0 0. mm. Sol.6 Possible p for maxima... i. e. 5 sin for st maxima sin sin D sin Dtan tan 8 y tan 0. 5 m. Sol.7 ( ) t P (48 0 ) t 8m 0. Sol.8 I0 4I P (y ) t m m P. 5 I0 0 D Shift.5.5 mm c 0 Sol.9 60 p must be 0 x x 8 7 5m (n + ) 0 x.5 or 7.5 to get minimum x 0 x x.5m Sol.0 5 n Possible values of n 5, 4,.. for each value of, we will get a circle with S as center. Sol. AB BC (n ) AB 00 m 8 c Sol. I A'B' I I A x 0 m 0 x B S S S 7.9

33 6 6 8 : Imin Imax 5 5 Sol. n n x D x n x () t D t xv y Sol.4 Let intensity of iniviual slit be I I0 4I with glass plate ( )t I I + I cos I I 0 ( + cos ) I I 0 cos v u f f 0 cm u 5 cm v mm v u Sol.9 Minima possible when (a) P (n + ) i. e. 0.75, 0.5, 0.5, 0.75 sin p y D tan sin tan , 5, 4, 4 4 (b) We nee to fin the initial P Sol.5 ( )t ; 0 5 r & 0 ( )t yc 6 g Sol.6 P ( ) t I Imax 4 60 or 60 ± n must lie between 0, ( ) (t t ) Sol.7 Ic I0 + I0 cos Imax 4I0. 0 5rD 0 60 P sin mm So, there will be no shift. Sol.0 Let D 5 P P ( )t 8 ( ) (t t ) Sol.8 S will have images which will act as sources an is similar to YDSE s v 6 cm S 7.0

34 Sol. b b Vwater V air V V air water µ µ water air Sol. For monochromatic light, Imax an fringe with is constant. so, we use white light to etermine central maximum. Sol. Case-I I I0+I0+ Case-II I I0+I0+ I I EXERCISE JEE ADVANCED Sol.4 At O, P SS if ( n ) I 0 I 0 I 0 I 0 0 minima n 0 maxima if 4., possible minimas.5,.5,..5. i.e. 8 points. Sol.5 90º 0º P sin sin 0 4 m D D m 00 So, possible maxima 99, 98,. 99 i.e. 599 maxima Sol.7 P nt nt cos(0º) 4I0 cos(90º) I0 (n t n t ) Sol.8 P (µ ) t 0 (µ ) t I I0 + I0 + I0cos I µ> µ Sol.9 P µt + t µ(t) P t y Dt y P D n (n n ) t n Sol.0 Central fringe will white as phase ifference 0 for all colours. We can't get completely ark fringe as all colours will not have phase ifference 0 at a single point. Sol. Imax I + ki + Icos; (cos ) I( + k + ) an k < Imin I( + k ) so Imax < I0 an Imin > 0 oesn't change. Fringes will shift towars covere slit. Sol. 0º / c 0º k I I + I + I I I0 4I If 90º ; If 0º; P I I I 0 8 k k cos(0º) ; I m ; 90º S 7.

35 Sol. For first ark fring on either sie sin or y D y yd Therefore istance between two ark fringes on either sie y yd Dark PREVIOUS YEARS QUESTIONS JEE ADVANCED D y by a factor of 4 6 or or the number of fringes in the same segment will increase by a factor of /. Therefore, number of fringes observe in the same segment 8 Note: since, if YDSE apparatus is immerse in a liqui of refractive inex, the wavelength, an thus the fringe with will ecrease times. Sin y/d Substituting that values, we have 6 Distance (600 0 mm)( 0 mm) (.0mm).4 mm Sol.4 At First minima, b sin First minimum P y or b or b D D or y or (i) b Now, at P (First minima) path ifference between the rays reaching from two eges (A an B) will be x b D A B D b D Dark b (Compare with x in YDSE) D or x [From eq. (i)] Corresponing phase ifference () will be.x,. D Sol.5 Fringe with, When the wavelength is ecrease from 600 nm to 400 nm, fringe with will also ecrease O y Sol.6 Path irrerence ue to slab shoul be integeral multiple of or x nλ or ( )t n n,, or t n For minimum value of t, n t.5 Sol.7 All points on a wavefront are at the same phase. c an f e f c e Hence the correct potion is (c) Sol.8 (A) (p, s) Intensity at P0 is maximum. It will continuously ecrease from P0 towars P. (B) (q) Path ifference ue to slap will be compensate by geometrical path ifference. Hence (P) 0 (c) (t) (P) an (P), (P) 4 4. When path 6 ifference increases from 0 to, intensity will ecrease from maximum to zero. Hence in this case, I(P) > I(P) > I(P0) I Sol.9 max I min I I I I I / I I / I 9 (Given) S 7.

36 Solving this, we have I A But I A A I 4 Correct option are (b) an () Sol.0 At P (irectly infrom of S) y Path ifference, X SP SP b b (b) b y.(b) Those wavelengths will be missing for which X, x S S x, b b 5 x b 5 5 Correct option are (a) an (c). Sol. The intensity of light is I() I cos where () ( sin ) (a) for 0º c v m an 50 m (50) 4 I() I0 cos 4 I 0 P y 0 [option (a)] b (b) For 90º or 00 (50) () an I() 0 (c) For 0º, 0 or I() I0 [option (c)] 0 Sol. Resultant intensity at P Ip IA + IB + IC P A 4 (PA) 90 4 () + + P B 4 (PB) 80 4 (.5) W/m cos 60º + IC cos 60º cos60º + 0 cos 60º Sol. Power receive by aperture A, PA I( r A ) 0 () (0.00) 0 5 W Power receive by aperture B, PB I( r B ) 0 () (0.00) W Only 0% of PA an PB goes to the original irection Hence, 0% of PA 0 6 P (say) an 0% of PB P (say) Path ifference create by slab x ( )t (.5 ) (000) 000Å Corresponing phase ifference,. x Now, resultant power at the focal point P P + P + P P cos (0 )(4 0 ) cos W Sol.4 (a)path ifference ue to the glass slab, x ( )t (.5 )t 0.5t Due to this slab, 5 re fringes have been shifte upwars. Therefore x 5re or0.5t (5) (7 0 7 m) t thickness of glass slab m S 7.

37 (b) Let be the refractive inex for green light then x ( ) Now the shifting is of 6 fringes of re light. Therefore, x 6re ( )t 6re 7 ( ) (6)(7 0 ) (c)in part (a), shifting of 5 bright fringes was equal to 0 m. Which implies that 5re 0 m (Here Fringe with) re 0 5 Now since green re m 0. 0 m D green re or green green re ( ) 7 re 7 0 green m green re (0.4 0.) 0 m m (0 + x.) (iii) (5 + ) Intensity at O is given I() or Imax Imax 4 4 cos cos Imax cos 4 Imax an since (iv) From Equation (iii) an (iv), we fin that 6 i.e., x t t 0 ()( ) 6(0.).8 or t m 9. m Sol.5.4 an.7 an let t be the thickness of each glass plates. Path ifference at O, ue to insertion of glass plates will be S S () () 6 th Minima O 5 th Minima x ( )t (.7.4)t 0.t (i) Now, since 5 th maxima (earlier) lies below O an 6 th minima lies above O. This path ifference shoul lie between 5 an 5 + So, let x 5 + Where < (ii) Due to the path ifference x, the phase ifference at O will S 7.4

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