10. WAVE OPTICS ONE MARK QUESTIONS

Transcription

1 1 10. WAVE OPTICS ONE MARK QUESTIONS 1. Define wavefront.. What is the shape of wavefront obtaine from a point source at a (i) small istance (ii) large istance? 3. Uner what conitions a cylinrical wavefront is obtaine? 4. What type of wavefront is obtaine when a plane wave is reflecte by a concave mirror? 5. Who propose the wave theory of light? 6. Name the physicist who experimentally stuie the interference of light for the first time. 7. What is interference of light? 8. What is the maximum intensity of light in Young s ouble slit experiment if the intensity of light emerging from each slit is I o? OR What is the intensity of light ue to constructive interference in Young s ouble slit experiment if the intensity of light emerging from each slit is I o? 9. Define fringe with. 10. Instea of using two slits as in Young s experiment, if two separate but ientical soium lamps are use, what is the result on interference pattern? 11. What is the effect on interference fringes when yellow light is replace by blue light in Young s ouble slit experiment? 1. How oes the fringe with in interference pattern vary with the wavelength of incient light? 13. What is the effect on the interference fringes in a Young s ouble-slit experiment when the monochromatic source is replace by a source of white light? 14. How oes the fringe with in interference vary with the intensity of incient light? 15. Which colour of light unergoes iffraction to maximum extent? 16. Name a factor which affects the resolving power of a microscope. 17. How will the iffraction pattern ue single slit change when violet light replaces green light? 18. Do all waves exhibit iffraction or only light? 19. We o not encounter iffraction effects of light in everyay observations. Why? 0. Why are iffraction effects ue to soun waves more noticeable than those ue to light waves? 1. Is the with of all seconary maxima in iffraction at slit same? If not how oes it vary?. What is resolving power of microscope? 3. What about the consistency of the principle of conservation of energy in interference an in iffraction? OR Does the law of conservation of energy hols goo in interference an in iffraction? 4. How can the resolving power of a telescope be increase? 5. Which phenomenon confirms the transverse nature of light? 6. What is meant by plane polarise light? 7. What is pass axis? 8. By what percentage the intensity of light ecreases when an orinary unpolarise (like from soium lamp) light is passe through a polaroi sheet? 9. Let the intensity of unpolarise light incient on P 1 be I. What is the intensity of light crossing polaroi P, when the pass-axis of P makes an angle 90 o with the pass-axis of P 1? 30. What shoul be the angle between the pass axes of two polarois so that the intensity of transmitte light form the secon polaroi will be maximum? 31. State Brewster s Law. 3. Write the relation between refractive inex of a reflector an polarising angle. 33. Define Brewster s angle (OR Polarising angle).

2 TWO MARKS QUESTIONS 1. State Huygens principle.. Name the wavefront obtaine when a plane wave passe through (i) a thin convex lens (ii) thin prism. 3. What is the shape of the wavefront in each of the following cases: (a) Light emerging out of a convex lens when a point source is place at its focus. (b) The portion of the wavefront of light from a istant star intercepte by the Earth. 4. What are coherent sources? Give an example. 5. Can two soium vapour lamps be consiere as coherent sources? Why? 6. Write the expression for fringe with in Young s ouble slit experiment. 7. What are the factors which affect the fringe with in Young s ouble slit experiment? 8. Let the fringe with in Young s ouble slit experiment be. What is the fringe with if the istance between the slits an the screen is ouble an slit separation is halve? 9. What is iffraction of light? Give an example. 10. Mention the conitions for iffraction minima an maxima. 11. Give the graphical representation to show the variation of intensity of light in single slit iffraction. 1. Mention the expression for limit of resolution of microscope. 13. Write the expression for limit of resolution of telescope. 14. Give the two methos of increasing the resolving power of microscope. 15. Write the mathematical expression for Malus law. Explain the terms. 16. Represent polarise light an unpolarise light. 17. Unpolarise light is incient on a plane glass surface. What shoul be the angle of incience so that the reflecte an refracte rays are perpenicular to each other? (For glass refractive inex = 1.5). OR What is the Brewster angle for air to glass transition? (For glass refractive inex = 1.5). 18. In a Young s ouble slit experiment, the angular with of a fringe forme on istant screen is The wavelength of light use is 6000 Ǻ. What is the spacing between the slits? 19. A beam of unpolarise is incient on an arrangement of two polarois successively. If the angle between the pass axes of the two polarois is 60 0, then what percentage of light intensity emerges out of the secon polaroi sheet? 0. Assume that light of wavelength 5000Å is coming from a star. What is the limit of resolution of a telescope whose objective has a iameter of 5.08m? THREE MARKS QUESTIONS 1. Using Huygen s wave theory of light, show that the angle of incience is equal to angle of reflection in case of reflection of a plane wave by a plane surface.. Illustrate with the help of suitable iagram, action of the following when a plane wavefront incients. (i) a prism (ii) a convex lens an (iii) a concave mirror. (each three marks) 3. Briefly escribe Young s experiment with the help of a schematic iagram. 4. Distinguish between interference of light an iffraction of light. 5. Briefly explain Polarisation by reflection with the help of a iagram. 6. Show that the refractive inex of a reflector is equal to tangent of the polarising angle. OR Arrive at Brewster s law. 7. What are Polarois? Mention any two uses of polarois. FIVE MARKS QUESTIONS 1. Using Huygen s wave theory of light, erive Snell s law of refraction.. Obtain the expressions for resultant isplacement an amplitue when two waves having same amplitue an a phase ifference superpose. Hence give the conitions for constructive an estructive interference. OR Give the theory of interference. Hence arrive at the conitions for constructive an estructive interferences.

3 3. Derive an expression for the with of interference fringes in a ouble slit experiment. 4. Explain the phenomenon of iffraction of light ue to a single slit an mention of the conitions for iffraction minima an maxima. FIVE MARKS NUMERICAL PROBLEMS 1. A monochromatic yellow light of wavelength 589nm is incient from air on a water surface. What are the wavelength, frequency an spee of a refracte light? Refractive inex of water is In a ouble slit experiment angular with of a fringe is foun to be 0. o on a screen place 80 cm away. The wave length of light use is 600 nm. Fin the fringe with. What will be the angular with of the fringe if the entire experimental apparatus is immerse in water? Take refractive inex of water to be 4/3. 3. A beam of light consisting of two wavelengths 650 nm an 50 nm, is use to obtain interference fringes in Young s ouble slit experiment with D = 60 cm an = 1 mm. a) Fin the istance of thir bright fringe on the screen from central maximum for wavelength 650nm. b) What is the least istance from the central maximum where the bright fringes ue to both the wavelengths coincie? 4. In Young s ouble-slit experiment using monochromatic light of wavelength λ, the intensity of light at a point on the screen where path ifference is λ, is K units. What is the intensity of light at a point where path ifference is (i) λ/3 (ii) λ/? 5. A parallel beam of light of wavelength 500 nm falls on a narrow slit an the resulting iffraction pattern is observe on a screen 1.5 m away. It is observe that the first minimum is at a istance of.5 mm from the centre of the screen. Fin (i) the with of the slit an (ii) angular position of the first seconary maximum. 6. In a Young s ouble-slit experiment, the slits are separate by 0.8 mm an the screen is place 1.4 m away. The istance between the central bright fringe an the fourth bright fringe is measure to be 1. cm. Determine the wavelength of light use in the experiment. Also fin the istance of fifth ark fringe from the central bright fringe. 7. In Young s ouble slit experiment with monochromatic light an slit separation of 1mm, the fringes are obtaine on a screen place at some istance from the slits. If the screen is move by 5cm towars the 3 slits, the change in fringe with is 30 m. Calculate the wavelength of the light use. ************** ANSWERS FOR ONE MARK QUESTIONS 1. A locus of points, which oscillate in phase is calle a wavefront. OR A surface of constant phase is calle wavefront.. (i) Spherical wavefront (ii) Plane wavefront. 3. A cylinrical wavefront is obtaine at a small istance from a linear source of light. 4. Spherical wavefront (converging). 5. Christiaan Huygens. 6. Thomas Young. 7. The moification in the istribution of light energy ue to the superposition of two or more waves of light is calle interference of light. 8. Maximum intensity of light in Young s ouble slit experiment is 4I o 9. The istance between two consecutive bright (or two consecutive ark) fringes is calle fringe with.

4 10. Interference pattern isappears. 11. The fringe with ecreases. Since λ an λ is smaller for blue light than yellow light. 1. The fringe with is irectly proportional to the wavelength of incient light. 13. The central fringe is white. The fringe closest on either sie of the central white fringe is re an the farthest will appear blue. 14. The fringe with is not affecte by the intensity of incient light. 15. Re. 16. The wave length of light or refractive inex of meium between objective lens an the object. 17. The iffraction bans become narrower. 18. All the waves exhibit the phenomenon of iffraction. 19. Since the wavelength of light is much smaller than the imensions of most of the obstacles. 0. The wavelength of soun waves is comparable with the size of the obstacles whereas for light, the wavelength is much smaller than the imensions of most of the obstacles. 1. No. As the orer of the seconary maximum increases its with ecreases.. The resolving power of the microscope is efine as the reciprocal of the minimum separation of two points which are seen as istinct. 3. Interference an iffraction are consistent with the principle of conservation of energy. 4. Using objective of larger iameter. 5. Polarisation. 6. Plane polarise light is one which contains transverse linear vibrations in only one irection perpenicular to the irection of propagation. 7. When an unpolarise light wave is incient on a polaroi, the light wave will get linearly polarise with the electric vector oscillating along a irection perpenicular to the aligne molecules. This irection is known as the pass-axis of the polaroi %. 9. Zero. Since no light passes through the polarois when they are crosse o. 31. Brewster s Law: The refractive inex of a reflector is equal to tangent of the polarising angle. 3. n = tan i B, where n - refractive inex of the reflector an i B - polarising angle/brewster s angle. 33. Brewster s angle/polarising angle(i B ): The angle of incience for which the reflecte light is completely plane polarise is calle Brewster s angle. ANSWERS FOR TWO MARKS QUESTIONS 1. Each point of the wavefront is the source of a seconary isturbance an the wavelets emanating from these points sprea out in all irections with the spee of the wave. These wavelets emanating from the wavefront are calle as seconary wavelets an if we raw a common tangent to all these spheres, we obtain the new position of the wavefront at a later time.. (i) Spherical converging wavefront; (ii) Plane wavefront. 3. (a) Plane wavefront; (b) Plane wavefront. 4. The two sources are sai to be coherent if the phase ifference between the waves emitte by them at any point will not change with time. OR Any two sources continuously emitting waves having zero or constant phase ifference are calle coherent sources. Example: In Young s ouble slit experiment the two slits behave like coherent sources. 5. No, because the phase ifference between light coming from two inepenent sources continuously change. λd 6. The fringe with: β ; where wavelength of light, istance between the slits an D istance between the screen an the slits. 7. The wavelength of light, istance between the slits an the screen or slit separation. [any two] 4

5 λd λ D λd 8. Initial fringe with: β an the new fringe with: β' 4 4β Thus, the new fringe with becomes four times the initial. 9. The phenomenon of bening of light waves aroun the eges (or corners) of the obstacles an entering into the expecte geometrical shaow of the obstacle is calle iffraction of light. Example: Colours observe when a CD (Compact Disc) is viewe is ue to iffraction of light. 10. Conition for seconary maxima is 5 1 λ Angle of iffraction θ n+, where n = ±1, ±, ±3, a Conition for iffraction minima: Angle of iffraction θ n λ, Where n = ±1, ±, ±3,... a where is wavelength of light use an a is slit with. 11. GRAPHICAL REPRESENTATION for the variation of intensity of light in single slit iffraction is as shown in the ajacent iagram. 1. λ 1. Minimum separation OR Limit of resolution: min n sinβ where wavelength of light, n refractive inex of the meium between the object an the objective lens an β angle subtene by the object at the iameter of the objective lens at the focus of the microscope λ 1. λ 13. Expression for limit of resolution of telescope: Limit of resolution: Δθ = = a a where wavelength of light an a iameter of aperture of the objective. 14. Resolving power of a microscope can be increase (i) by choosing a meium of higher refractive inex an (ii) by using light of shorter wavelength. 15. I = I 0 cos, Where I is the intensity of the emergent light from secon polaroi (analyser), I 0 is the intensity of plane polarise light incient on secon polaroi after passing through first polaroi(polariser) an is the angle between the pass-axes of two polarois (analyser an polariser). 16. Unpolarize light is represente as shown in figure(a) an figure (b). [any one] Plane polarize light with vibrations parallel to the plane of the paper is shown in figure(c). Plane polarize light with vibrations perpenicular to the plane of the paper is as shown in figure(). [any one] 17. n = tan i B Brewster s angle for glass: i B = tan 1 (n) = tan 1 (1.5) = 56 o Given θ = 0.1 o π = = ra an wavelength of light = = 6000 Å = m 7 λ Spacing between the slits is = = m 3 θ Given θ = 60 o, Intensity of light incient on the polaroi = I o, Intensity of light transmitte through the polaroi I =? I = I 0 cos I = I 0 cos 60 o =I 0/4. Thus 5% of the light intensity is transmitte through the polarois. 0. Given wavelength of light = 5000 Å = m, Diameter of the objective= 5.08m

6 Limit of resolution: λ Δθ = a raians ANSWERS FOR THREE MARKS QUESTIONS: 1. Consier a plane wave AB incient at an angle i on a reflecting surface MN. If v represents the spee of the wave in the meium an if τ represents the time taken by the wavefront to avance from the point B to C then the istance BC = vτ, In orer to construct the reflecte wavefront, a sphere of raius = vτ, is rawn from the point A as shown in the ajacent figure. Let CE represent the tangent plane rawn from the point C to this sphere. AE = BC = vτ, ABC= CEA = 90 o, AC is common. Triangles EAC an BAC are congruent. i = r.. (i) Action of the prism when a plane wavefront incient on it: In ajacent figure, consier a plane wave passing through a thin prism. Since the spee of light waves is less in glass, the lower portion of the incoming wavefront which travels through the greatest thickness of glass will get elaye resulting in a tilt in the emerging plane wavefront. (ii) Action of the convex lens when a plane wavefront incient on it: In the ajacent figure, a plane wave incient on a thin convex lens; the central part of the incient plane wave traverses the thickest portion of the lens an is elaye the most. The emerging wavefront has a epression at the centre an therefore the wavefront becomes spherical (raius = f, focal length) an converges to the point focus F. (iii) Action of the concave mirror when a plane wavefront incient on it: In ajacent figure, a plane wave is incient on a concave mirror an on reflection we have a spherical wave converging to the focus F. 3. Young s experiment : Description with a schematic iagram S represents a pin hole illuminate by sunlight. The spherical wave front from S is incient on two pin holes S 1 an S which are very close to each other an equiistant from S. Then the pin holes S 1 an S act as two coherent sources of light of same intensity. The two sets of spherical wave fronts coming out of S 1 an S interfere with each other in such a way as to prouce a symmetrical pattern of varying intensity on the screen place at a suitable istance D. 4. Differences between interference of light an iffraction of light: INTERFERENCE DIFFRACTION 1 Interference fringes have equal with. Diffraction bans have unequal with. (with of seconary maxima ecreases with increase in orer) Interference is ue to the superposition of two waves originating from two coherent sources It is ue to the superposition of seconary wavelets originating from ifferent parts of single slit.

7 7 3 Intensity of all bright fringes is equal an Intensity of ark fringes is zero. 4 At an angle of λ/a, maximum intensity for two narrow slits separate by a istance a is foun. 5 In an interference pattern there is a goo contrast between ark an bright fringes. Intensity of central maximum is highest, Intensity of seconary maxima ecreases with increase in orer. At an angle of λ/a, the first minimum of the iffraction pattern occurs for a single slit of with a. In a iffraction pattern the contrast between the bright ban an ark ban is comparatively lesser. 5. POLARIZATION BY REFLECTION: It is foun that when a beam of orinary light is reflecte by the surface of a transparent meium like glass or water, the reflecte light is partially polarize. The egree of polarization epens on the angle of incience. As the angle of incience is graually increase from a small value, the egree of polarization also increases. At a particular angle of incience the reflecte light is completely plane polarize. This angle of incience is calle Brewster s angle or polarizing angle (i B ). If the angle of incience is further increase, the egree of polarization ecreases. 6. From Snell s law, n = sin i sin r = sin ib sin r, since i = i B. For Brewster s angle of incience, r + i B = 90 sin ib sin ib n = sin (90 o i ) cos i B B r = 90 i B Refractive inex of reflector: n = tan i B 7. Polarois are the evices use to prouce plane polarise light. Uses of polarois: 1) To control the intensity of light in sunglasses, winowpanes, etc.. ) In photographic cameras an 3D movie cameras. ANSWERS FOR FIVE MARKS QUESTIONS: 1. Derivation of Snell s law of refraction. Let PP represent the surface separating meium-1 an meium-. Let v 1 an v be the spee of light in meium-1 an meium- respectively. Consier a plane wave front AB incient in meium-1 at angle i on the surface PP. Accoring to Huygens principle, every point on the wave front AB is a source of seconary wavelets. Let the seconary wavelet from B strike the surface PP at C in a time. Then BC = v 1. The seconary wavelet from A will travel a istance v as raius; raw an arc in meium. The tangent from C touches the arc at E. Then AE = v an CE is the tangential surface touching all the spheres of refracte seconary wavelets. Hence, CE is the refracte wave front. Let r be the angle of refraction. In the above figure, BAC = i = angle of incience an ECA = r = angle of refraction BC = v 1 an AE = v BC AE From triangle BAC, sin i an from triangle ECA, sin r AC AC

8 sin i BC/AC BC v v sin r AE/AC AE v v Since v 1 is a constant in meium-1 an v is a constant in meium-, sin i sin r v 1 constant..( * ) v c c Now, refractive inex (n) of a meium: n = or v =, where c spee of light in vacuum. v n c c v For the first meium: v 1 = an for the secon meium: v = 1 n n n v n sin i n ( * ) becomes sin r n 1 1 or 1 1 n sin i = n sin r. This is the Snell s law of refraction.. THEORY OF INTERFERENCE: Expression for the amplitue of resultant isplacement an intensity If the isplacement prouce by source S 1 is given by y 1 = a cos(t) Then the isplacement prouce by S woul be y = a cos(t + ), where is the phase ifference between the two waves. The resultant isplacement: y = y 1 + y = [ a cos (t) + a cos (t + )] = a [cos (t + )+ cos (t)] t + = a cos cos C+D ; Using cosc + cosd = cos.cos C D = a cos cos ωt + The amplitue of the resultant isplacement is a cos Conitions for constructive Interference: If the two coherent sources S 1 an S vibrating in phase, then at an arbitrary point P, The phase ifference: = 0,, 4. [OR path ifference: = n, (Where n = 0, 1,, 3..)] constructive interference takes place leaing to maximum intensity = 4I 0 an Resultant amplitue = a Conitions for estructive Interference: 1 If the point P is such that the phase ifference: =, 3, 5 [OR path ifference: δ = n + λ (Where n = 0,1,, 3...)], estructive interference takes place, leaing to zero amplitue an zero intensity. 3. Derivation of expression for fringe with: In the ajacent figure S 1 an S represent two coherent source (slits in Young s ouble slit experiment) separate by a istance. Let a screen be place at a istance D from the coherent sources. The point O on the screen is equiistant from S 1 an S so E / that the path ifference between the two light waves from S 1 an S reaching O is zero. Thus the point O has maximum intensity. Consier a point P at a istance from O. The path ifference between the light waves from S 1 an S reaching the point P is = S P S 1 P x / F SP SF FP D x From the figure, S1P S1E EP D x Similarly,

9 SP S1P D x D x D + x x D x x = x 4 4 x i.e., SP S1P SP + S1P = x OR SP S1P SP S1P Since P is very close to O an << D, SP + S1P D Path ifference: SP S1P = x = x (1) D D Equation (1) represents the path ifference between light waves from S 1 an S superposing at the point P. For bright fringe or maximum intensity at P, the path ifference must be multiple of, where is the wavelength of the light use. i.e., S P S 1 P = n λ ; n = 0, 1,... x λ D From equn.(1), = n λ or x n D The istance of the n th D bright fringe from the centre O of the screen is xn n The istance of (n + 1) th D bright fringe from the centre of the screen is xn 1= n+1 λ D λ D λ D The fringe with, β = xn+1 x n = (n+1) n λ D = β = 4. DIFFRACTION OF LIGHT AT SINGLE SLIT: When single narrow slit illuminate by a monochromatic light source, a broa pattern with a central bright region is seen. On both sies, there are alternate ark an bright regions; the intensity becomes weaker away from the centre. 9 A parallel beam of light falling normally on a single slit LN of with a. The iffracte light goes on to meet a screen. The mipoint of the slit is M. A straight line through M perpenicular to the slit plane meets the screen at C. The straight lines joining P to the ifferent points L, M, N, etc., can be treate as parallel, making an angle θ with the normal MC. This is to ivie the slit into smaller parts, an a their contributions at P with the proper phase ifferences. Different parts of the wavefront at the slit are treate as seconary sources. Because the incoming wavefront is parallel to the plane of the slit, these sources are in phase. The path ifference between the two eges of the slit N an P is NP LP = NQ = a sin θ a θ At the central point C on the screen, the angle θ is zero. The path ifference is zero an hence all the parts of the slit contribute in phase. This gives maximum intensity at C, the central maximum. 1 λ Seconary maxima is forme at θ n+, where n = ±1, ±, ±3,.. a Minima (zero intensity) is forme at θ n λ, Where n = ±1, ±, ±3,... a ANSWERS FOR FIVE MARKS NUMERICAL PROBLEMS:

10 10 1. For refracte light, wavelength: λ = λ/n = /1.33 = m As frequency remain unaffecte on entering another meium = = = c/λ = Hz Spee of light in water, v = c/n = m/s. Angular fringe with: θ = λ = π 0.o = = ra. λ D λ Fringe with β = = D = =.79 mm. When entire experimental apparatus is immerse in water, wavelength of light λ = λ /n o λ' λ 0. o Hence angular fringe with in water, θ = n 4/3 3. Given 1 = 650nm= m an = m. a) The istance of n th bright fringe on the screen from central maximum, x n = The istance of thir bright fringe on the screen from central maximum x 3 = = m = 1.17mm b) For least istance x, the n th bright fringe ue to longer wavelength ( 1 ) coincies with the (n+1) th bright fringe ue to shorter wavelength ( ). or n = (n+1) n = 4 Require least istance, x 4 = = 1.56 mm 4. If the phase ifference between the two waves is, then the intensity at that point is I= 4I 0 cos. Given path ifference = λ, the corresponing phase ifference is. Thus, I = 4 I 0 cos π = 4 I 0 = K (given). (i) Given path ifference = λ/3 phase ifference = /3 The intensity at that point is I = 4I 0 cos π/3 = K(1/) = K/4. (ii) Given path ifference = λ/ phase ifference =. The intensity at that point is I = 4I 0 cos π = Given = 500 nm = m, D = 1.5 m, x =.5 mm = m. Angular position of the first minimum, tan θ θ = 7 λ 510 (i) The with of the slit, a = = m. 3 θ 10 1 λ (ii) Seconary maxima is forme at θ n+ a x.510 D = 10 3 ra. (Assuming θ to be small)

11 11 For the first seconary maximum n = 1, Thus, the angular position of the first seconary maximum, θ 3 λ 7 a = = ra. 6. Given D = 1.4 m, x 4 = 1.cm = m, =0.8 mm= m, =? an for fifth ark fringe x =? n λ D th Distance of n bright fringe from central bright fringe : x n = x n 7 Wavelength of light : λ = = = 6 10 m = 600nm n D λ D Distance of ark fringe from central bright fringe : x = n n = 4 for fifth ark fringe, x = 4 + = m = 1.35 cm Given = 1 mm = 10 3 m. Let the initial istance of the screen of the screen from the slits be D. When the screen is move 5cm towars the slits the fringe with ecreases by 30m. D = D 5 10 m an = m. λd Initial fringe with: β.(1) The new fringe with: β Using equn.(1) in RHS of equn.(), ' λ D 5 10 λ λ λd β () λ β 3010 β λ λ = 610 m 600 nm *******************************************************************************