Physical optics
1. Physical Optics
2. Geometrical Optics deals with particle nature of light. Physical Optics deals with wave nature of light.
3. Clark Maxwell first established that EM wave is not a mechanical wave. In 1831, Michael Faraday invented EM induction.
4. In 1864, James Clark Maxwell proposed opposite effect of Faraday.
5. If alternate electric field vector (𝐸) and magnetic field vector (𝐵)vibrates perpendicularly then a wave perpendicular on both (𝐸) and (𝐵) propagates at 3X108 ms-1 which is called electromagnetic wave. Speed of this wave, C = f𝜆
6. In vacuum, if c = speed of light, E0 = peak value of electric field B0 = peak value of magnetic field In t sec, E = E0 sin (x – ct) B = B0 sin (x – ct)
7. From Maxwell’s theory, E0 = CB0 Magnitude of c in vacuum for all types of EM wave is constant which not only depends on λ and f.
8. Heinrich Hertz in 1888 produced an EM wave of small wave length from an oscillated electric coil. Marconi researched in the field of radio broadcasting.
9. Characteristics of EM wave: - In vacuum its speed is 3X108 ms-1.
10. Pointing vector: EM wave can transfer energy from one point to another. Amount of energy passing through a unit area perpendicular to the motion of EM wave is called Poyinting vector. Its denoted by S.
11. Radio 10-1m to 105 Oscillating electric circuit Small change in energy in the electron of an atom Radio communication Compare seven EM waves Wave Range of 𝝀 Source Cause Uses Micro 10-1m to 10-3 IR 10-3m to 4X10-7 Visible 3.9X10-7m to 7.8X 10-7 UV 3.9X10-7m to 3X10-9 m X – ray 3.9X10-9m to 10-11 Gamma 10-11m to 10-15
12. Disturbance which transforms energy without displacing the particles is called wave.
13. Wave front: What is wave front? The locus of the particle of a wave having same phase is called wave front.
14. A surface touching these secondary wavelets tangentially in the forward direction at any instant gives the new wave front at that instant. This is called secondary wave front
15. Wave front is of two types:
16. b) Plane wave front: If the locus of the particles in a wave having same phase is plane, then the wave front is plane wave front. a) Spherical wave front: If the locus of the particles in a wave having same phase is spherical, then the wave front is spherical wave front. As the distance from the origin of waves goes on increasing, the curvature of the spherical wave front goes on decreasing. At a large distance from the source, the wave front becomes very nearly plane like shape.
17. Huygens's principle: To explain interference, diffraction and polarization Huygen gave two assumption as: 1. Each point on a wave front is a source of a new disturbance called second wave which travels with the same velocity as that of original waves’ provided the medium is same.
18. Huygens's principle: 2. The position and the shape of the new wave front at any instance of time t is given by the envelope or tangential surface of the secondary wavelets at that instance.
19. Explanation: Suppose for the source S, AB is a spherical wave front. According to Huygens’s principle each point of AB will be a secondary source. In the diagram, P1, P2, P3 etc are secondary source.
20. Application of Huygens's Principle: Law of reflection:
21. Law of refraction:
22. Super Position of waves:
23. Same & opposite Phase
24. Coherent source: The sources of light which emits continuous light waves of the same wavelength, same frequency and in same phase or having a constant phase difference are called coherent sources. Laser light is highly coherent and monochromatic.
25. Interference of Light.
26. Interference Fringe
27. Conditions for Interference • Sources should be coherent. • Sources should be very fine and small • Sources should be very close to each other • Amplitude of the two sources should be very close to each other • For alternate bright and dark points, the path difference between the waves should be even & odd multiples respectively.
28. Characteristics of Interference • Interference is produced when two coherent sources superposed at a point in a medium. • Normally the width of the interference fringes are equal. • Distance between the bright & dark fringes are equal. • The intensity of all the bright fringes are equal
29. Relation between phase difference & Path difference 𝛿 = 2𝜋 𝜆 𝑥
30. Phase Difference
31. Constructive Destructive Def (i) When the waves meets a point with same phase, constructive interference is obtained at that point (i.e. maximum light) i) When the wave meets a point with opposite phase, destructive interference is obtained at that point (i.e. minimum light) Phase difference ii) φ = 00 or 2nπ ii) φ = 1800 or (2n – 1) π; n = 1, 2, …. Or, (2n+1)π; n = 0, 1, 2 ……. Two Types of Interference
32. Young’s Double Slit Experiment
33. Young’s Double Slit Experiment
34. Mathematical Analysis of Young’s Double Slit Experiment y1 = a sin 2𝜋 𝜆 vt y2 = a sin 2𝜋 𝜆 (vt+x) y = a sin 2𝜋 𝜆 vt + a sin 2𝜋 𝜆 (vt+x) y = 2a cos 𝜋𝑥 𝜆 vt Bright fringe & Dark fringe O Q R x P Screen S1 S2 d D
35. Fringe gap and Fringe width PQ = x - 𝒅 𝟐 & PR = x + 𝒅 𝟐 S2P2 – S1P2 = 𝐃 𝟐 + x + 𝐝 𝟐 𝟐 − 𝐃 𝟐 + x − 𝐝 𝟐 𝟐 = 𝟐𝐱𝐝 S2P – S1P S2P + S1P = 𝟐𝒙𝒅 S2P – S1P = 𝟐𝒙𝒅 S2P + S1P = 𝟐𝒙𝒅 𝟐𝑫 As S2P ≈ S1P ≈ D O Q R x P Screen S1 S2 d D
36. Path difference, S2P – S1P = 𝟐𝒙𝒅 𝟐𝑫 = 𝒙𝒅 𝑫 For maximum brightness at P 𝒙𝒅 𝑫 = 𝒏𝝀 Here, n = 0, 1, 2, 3, …… For central max, n = 0
37. From O to any side, for first, second, third etc. bright fringe n = 1, 2, 3 etc. If from O to nth bright fringe is xn then 𝒙 𝒏 𝒅 𝑫 = 𝒏𝝀 Or, 𝐱 𝐧 = 𝐧 𝛌 𝐃 𝐝 For (n+1)th bright fringe from O , 𝐱 𝐧+𝟏 = (𝐧 + 𝟏) 𝛌 𝐃 𝐝 Difference between two consecutive bright fringe, 𝐱 𝐧+𝟏 − 𝒙 𝒏 = 𝐧 + 𝟏 𝛌 𝐃 𝐝 − 𝐧 𝛌 𝐃 𝐝 = 𝛌 𝐃 𝐝
38. Similarly Path Difference between two consecutive dark fringe, 𝐱 𝐧+𝟏 − 𝒙 𝒏 = 𝛌 𝐃 𝐝 Fringe width Fringe width Dark fringe Bright fringe Fringe gap So, Fringe width, x = 𝛌 𝐃 𝟐𝐝 This equation is used when one fringe is mentioned
39. About interference • For interference, distance between the centre of two bright or dark fringe or fringe width are same • The more the D value the more the fringe width • The less the ‘d’ the more the fringe width
40. Diffraction
41. Diffraction: Fresnel diffraction Fraunhofer diffraction (i) If either source or screen or both are at finite distance from the diffracting device (obstacle or aperture), the diffraction is called Fresnel type. (ii) Common examples : Diffraction at a straight edge, narrow wire or small opaque disc etc. (i) In this case both source and screen are effectively at infinite distance from the diffracting device. (ii) Common examples : Diffraction at single slit, double slit and diffraction grating
42. a sinθ = (2n + 1) λ/2 For a bright point from edge S1 and S2 a sinθ = nλ And for a dark point from edge S1 and S2 a θ θ S1 S2
43. Diffraction Grating The special device for the production of diffraction is called Grating. It consists of a very large number of narrow slits of equal width side by side. Grating Constant, d = a + b Distance from the starting of a slit to the starting of the next slit is called Grating Constant
44. In the length ‘d’ of the grating, number of line = 1 So, the number of lines in unit length, N = 1 𝑑 = 1 𝑎+𝑏
45. Polarization of light
46. Polarization of Light
47. Some Terms related to Polarization of Light • Polarized Light • Unpolarized Light • Plane Polarized Light • Plane of vibration • Polarising angle • Plane of Polarization • Double refraction • Optic axis • Principal plane • Principal section
48. Important Mathematical Problems Type 1: Electromagnetic Wave E = E0sin(x – ct) Equation to be used B = B0sin(x – ct) Relation between electric & magnetic field, Bo = 𝑬 𝒐 𝒄
49. Type 2: Light speed C = f𝜆 = 1 ∈0 𝜇0 Type 3: Light speed, wave length & RI a 𝜇b= 𝐶 𝑎 𝐶 𝑏 = 𝜆 𝑎 𝜆 𝑏 a 𝜇b= 𝜇 𝑏 𝜇 𝑎
50. Speed of light in water is 2.22X108 ms-1. wavelength of sodium light in vacuum is 5892 Å then determine wavelength of that light in water. Hints: 𝑪 𝟎 𝑪 𝒘 = 𝝀 𝟎 𝝀 𝒘
51. Path difference between two points of a wave is 5𝜆 2 then determine the phase difference. 𝝅 Type 4: Phase difference & path difference Hints: 𝛿 = 2𝜋 𝜆 𝑥 Phase difference between two points of a wave is 𝜋 2 then determine path difference. 𝝀 𝟒
52. Type 5: distance between central bright to nth fringe 𝒙 𝒏 = 𝒏𝑫𝝀 𝒅 Where, n = number of fringe D = distance between the slit & the screen 𝜆 = wavelength d = distance between two slits This equation may be used to determine distance from central max to any fringe, screen distance, wavelength, distance between two slits, no. of fringe Type 6: width of the bright fringe 𝚫𝒙 = 𝑫𝝀 𝟐𝒅
53. Mathematical problems • In a Young’s double slit experiment, distance between two slits is 0.4mm. At 1m distance a fringe is created where the distance between the central max to 12th bright fringe is 9.3mm. Determine the wavelength of the wave. [3100 Å] • In a Young’s double slit experiment, the separation between the slits is 0.10 m, the wavelength of light used is 500 nm and the interference pattern is observed on a screen 1.0m away. Find the separation between successive bright bands. 𝒙 = 𝑫𝝀 𝒅
54. • In a Young’s double slit experiment, fringe width is found is 0.4mm. Keeping the arrangement same if the experiment is done in water then what will be the fringe width? Refractive index of water is 𝟒 𝟑 • 𝝁 𝒘 = ∆𝒙 ∆𝒙/ where, ∆𝒙/ is the new fringe width
55. An interference spectra is formed in the screen at a distance of 1m from two slits having separation of 0.4 mm. If the wavelength of light is 500 Å then a) Find the distance between two successive bright bands and b) What is the distance between two successive dark bands. a) b) 2x
56. Find 2d A double slit experiment is performed with light of wavelength 589nm and he interference pattern is observed on a screen 100 cm away. The tenth bright fringe has its centre at a distance of 10 mm from the central maximum. Find the separation between the slits
57. Condition for bright point: a sin𝜽 = (𝟐𝒏 + 𝟏) 𝝀 𝟐 Type 4: Diffraction Condition for dark point: a sin𝜽 = 𝒏𝝀 These equations are used to determine width of the slit, number of fringe, diffraction angle and wavelength For grating constant: d sin𝜽 = 𝒂 + 𝒃 𝒔𝒊𝒏𝜽 = 𝒔𝒊𝒏𝜽 𝑵 = 𝒏𝝀 Where, N = 𝟏 𝒂+𝒃
58. In a Fraunhauffer class diffraction experiment due to a single slit a light of wavelength of 5600Å is used. Determine the angle of diffraction for the first dark band. [width of the slit = 0.2 mm] We know, a sinθ = nλ Ans: 0.160
59. In a Fraunhauffer class diffraction light of wavelength of 5600Å is used. Find the angle of diffraction of the second maxima a sinθ = nλ θ = 300
60. A light of wavelength of 8X10-7 m incident on a plane grating produces the angle of diffraction of 300 for the first order. What is the number of lines per cm in the grating?
61. There are 4200 lines per cm in a grating. If parallel rays of sodium light are incident normally on it, then the second order spectral lines produces an angle of 300. Calculate the wavelength of sodium light We know, (a+b)Sinθn = nλ λ = 595 m
62. 1. In optics lab, Raihan incident a monochromatic light of 600 nm through a 2μm wide slit perpendicularly. H thought that he would see nine bright points. c) Determine angular distance between first order bright points. d) Analyze whether he could see nine bright points or not!
63. 2. In a Young’s double slit experiment distance between the slits is 0.3mm. Distance from the slit to the screen is 1m. While experimenting in air, distance between the central maxima to 8th bright fringe was found 6.2mm. The whole system is kept in water. c) Determine wavelength of light used in the experiment. d) In water, will there be any change in fringe width? Analyze.
64. 3. In Young’s double slit experiment following arrangement is shown. Wavelength of the light used 5800 Ǻ 1m 2mm 20cm c) Determine the wavelength of light used I the stem. d) If the screen distance is increased by 20 cm then will you get the fringe of same width? Analyze.
65. 1. Electromagnetic wave 2. Wave theory of light 3. Electromagnetic theory 4. Poynting vector 5. Wave front 6. Diffraction grating 7. Plane transmission grating 8. Grating constant 9. Polarized Light 10.Unpolarized Light 11.Plane Polarized Light 12.Plane of vibration 13.Polarising angle 14.Plane of Polarization 15.Double refraction 16.Optic axis 17.Principal plane 18.Principal section
66. 1. Compare 7 electromagnetic waves. 2. Write down the characteristics of electromagnetic waves. 3. What do you mean by 1 light year? 4. State Huygens’s principle of formation of wave front. 5. What is interference of light? Write down the conditions and characteristics of interference of light.
67. 6. Write down the difference between constructive and destructive interference. 7. What do you mean by coherent source? 8. Show relation between phase difference and path difference. 9. What is diffraction of light? Write down the condition for diffraction of light.
68. 10. Write down the difference between Fraunhoffer and Fresnel Class diffraction. 11. Write down the difference between Interference and diffraction. 12. Two same type of light source can’t produce interference – explain. 13. If a thin glass plate is placed on the path of one source then will there be any change in fringe? Explain your answer. 14. Longitudinal waves have no polarization – Explain.
69. 15. Light year through glass is 6.27X1012 km – What do you mean by this? 16. No source is coherent in nature – Explain.
70. Facts for MCQ 19. When the waves are coherent? 20. Conditions for interference of light. 21. When two coherent monochromatic light source forms constructive interference then phase difference becomes __________ 22. What is the reason for keeping two slits in case of Young’s double slit experiment? 23. Phase difference between the two points of a wave is 𝜋 2 then path difference between the point will be _______
71. Comparison between different Light Theory
72. Sl. No. Phenomena Corpuscular Wave EM wave Quantum Dual 1. Rectilinear Propagation √ √ √ √ √ 2. Reflection √ √ √ √ √ 3. Refraction √ √ √ √ √ 4. Dispersion X √ √ X √ 5. Interference X √ √ X √ 6. Diffraction X √ √ X √ 7. Polarization X √ √ X √ 8. Photoelectric effect X X X √ X
1. Physical Optics
2. Geometrical Optics deals with particle nature of light. Physical Optics deals with wave nature of light.
3. Clark Maxwell first established that EM wave is not a mechanical wave. In 1831, Michael Faraday invented EM induction.
4. In 1864, James Clark Maxwell proposed opposite effect of Faraday.
5. If alternate electric field vector (𝐸) and magnetic field vector (𝐵)vibrates perpendicularly then a wave perpendicular on both (𝐸) and (𝐵) propagates at 3X108 ms-1 which is called electromagnetic wave. Speed of this wave, C = f𝜆
6. In vacuum, if c = speed of light, E0 = peak value of electric field B0 = peak value of magnetic field In t sec, E = E0 sin (x – ct) B = B0 sin (x – ct)
7. From Maxwell’s theory, E0 = CB0 Magnitude of c in vacuum for all types of EM wave is constant which not only depends on λ and f.
8. Heinrich Hertz in 1888 produced an EM wave of small wave length from an oscillated electric coil. Marconi researched in the field of radio broadcasting.
9. Characteristics of EM wave: - In vacuum its speed is 3X108 ms-1.
10. Pointing vector: EM wave can transfer energy from one point to another. Amount of energy passing through a unit area perpendicular to the motion of EM wave is called Poyinting vector. Its denoted by S.
11. Radio 10-1m to 105 Oscillating electric circuit Small change in energy in the electron of an atom Radio communication Compare seven EM waves Wave Range of 𝝀 Source Cause Uses Micro 10-1m to 10-3 IR 10-3m to 4X10-7 Visible 3.9X10-7m to 7.8X 10-7 UV 3.9X10-7m to 3X10-9 m X – ray 3.9X10-9m to 10-11 Gamma 10-11m to 10-15
12. Disturbance which transforms energy without displacing the particles is called wave.
13. Wave front: What is wave front? The locus of the particle of a wave having same phase is called wave front.
14. A surface touching these secondary wavelets tangentially in the forward direction at any instant gives the new wave front at that instant. This is called secondary wave front
15. Wave front is of two types:
16. b) Plane wave front: If the locus of the particles in a wave having same phase is plane, then the wave front is plane wave front. a) Spherical wave front: If the locus of the particles in a wave having same phase is spherical, then the wave front is spherical wave front. As the distance from the origin of waves goes on increasing, the curvature of the spherical wave front goes on decreasing. At a large distance from the source, the wave front becomes very nearly plane like shape.
17. Huygens's principle: To explain interference, diffraction and polarization Huygen gave two assumption as: 1. Each point on a wave front is a source of a new disturbance called second wave which travels with the same velocity as that of original waves’ provided the medium is same.
18. Huygens's principle: 2. The position and the shape of the new wave front at any instance of time t is given by the envelope or tangential surface of the secondary wavelets at that instance.
19. Explanation: Suppose for the source S, AB is a spherical wave front. According to Huygens’s principle each point of AB will be a secondary source. In the diagram, P1, P2, P3 etc are secondary source.
20. Application of Huygens's Principle: Law of reflection:
21. Law of refraction:
22. Super Position of waves:
23. Same & opposite Phase
24. Coherent source: The sources of light which emits continuous light waves of the same wavelength, same frequency and in same phase or having a constant phase difference are called coherent sources. Laser light is highly coherent and monochromatic.
25. Interference of Light.
26. Interference Fringe
27. Conditions for Interference • Sources should be coherent. • Sources should be very fine and small • Sources should be very close to each other • Amplitude of the two sources should be very close to each other • For alternate bright and dark points, the path difference between the waves should be even & odd multiples respectively.
28. Characteristics of Interference • Interference is produced when two coherent sources superposed at a point in a medium. • Normally the width of the interference fringes are equal. • Distance between the bright & dark fringes are equal. • The intensity of all the bright fringes are equal
29. Relation between phase difference & Path difference 𝛿 = 2𝜋 𝜆 𝑥
30. Phase Difference
31. Constructive Destructive Def (i) When the waves meets a point with same phase, constructive interference is obtained at that point (i.e. maximum light) i) When the wave meets a point with opposite phase, destructive interference is obtained at that point (i.e. minimum light) Phase difference ii) φ = 00 or 2nπ ii) φ = 1800 or (2n – 1) π; n = 1, 2, …. Or, (2n+1)π; n = 0, 1, 2 ……. Two Types of Interference
32. Young’s Double Slit Experiment
33. Young’s Double Slit Experiment
34. Mathematical Analysis of Young’s Double Slit Experiment y1 = a sin 2𝜋 𝜆 vt y2 = a sin 2𝜋 𝜆 (vt+x) y = a sin 2𝜋 𝜆 vt + a sin 2𝜋 𝜆 (vt+x) y = 2a cos 𝜋𝑥 𝜆 vt Bright fringe & Dark fringe O Q R x P Screen S1 S2 d D
35. Fringe gap and Fringe width PQ = x - 𝒅 𝟐 & PR = x + 𝒅 𝟐 S2P2 – S1P2 = 𝐃 𝟐 + x + 𝐝 𝟐 𝟐 − 𝐃 𝟐 + x − 𝐝 𝟐 𝟐 = 𝟐𝐱𝐝 S2P – S1P S2P + S1P = 𝟐𝒙𝒅 S2P – S1P = 𝟐𝒙𝒅 S2P + S1P = 𝟐𝒙𝒅 𝟐𝑫 As S2P ≈ S1P ≈ D O Q R x P Screen S1 S2 d D
36. Path difference, S2P – S1P = 𝟐𝒙𝒅 𝟐𝑫 = 𝒙𝒅 𝑫 For maximum brightness at P 𝒙𝒅 𝑫 = 𝒏𝝀 Here, n = 0, 1, 2, 3, …… For central max, n = 0
37. From O to any side, for first, second, third etc. bright fringe n = 1, 2, 3 etc. If from O to nth bright fringe is xn then 𝒙 𝒏 𝒅 𝑫 = 𝒏𝝀 Or, 𝐱 𝐧 = 𝐧 𝛌 𝐃 𝐝 For (n+1)th bright fringe from O , 𝐱 𝐧+𝟏 = (𝐧 + 𝟏) 𝛌 𝐃 𝐝 Difference between two consecutive bright fringe, 𝐱 𝐧+𝟏 − 𝒙 𝒏 = 𝐧 + 𝟏 𝛌 𝐃 𝐝 − 𝐧 𝛌 𝐃 𝐝 = 𝛌 𝐃 𝐝
38. Similarly Path Difference between two consecutive dark fringe, 𝐱 𝐧+𝟏 − 𝒙 𝒏 = 𝛌 𝐃 𝐝 Fringe width Fringe width Dark fringe Bright fringe Fringe gap So, Fringe width, x = 𝛌 𝐃 𝟐𝐝 This equation is used when one fringe is mentioned
39. About interference • For interference, distance between the centre of two bright or dark fringe or fringe width are same • The more the D value the more the fringe width • The less the ‘d’ the more the fringe width
40. Diffraction
41. Diffraction: Fresnel diffraction Fraunhofer diffraction (i) If either source or screen or both are at finite distance from the diffracting device (obstacle or aperture), the diffraction is called Fresnel type. (ii) Common examples : Diffraction at a straight edge, narrow wire or small opaque disc etc. (i) In this case both source and screen are effectively at infinite distance from the diffracting device. (ii) Common examples : Diffraction at single slit, double slit and diffraction grating
42. a sinθ = (2n + 1) λ/2 For a bright point from edge S1 and S2 a sinθ = nλ And for a dark point from edge S1 and S2 a θ θ S1 S2
43. Diffraction Grating The special device for the production of diffraction is called Grating. It consists of a very large number of narrow slits of equal width side by side. Grating Constant, d = a + b Distance from the starting of a slit to the starting of the next slit is called Grating Constant
44. In the length ‘d’ of the grating, number of line = 1 So, the number of lines in unit length, N = 1 𝑑 = 1 𝑎+𝑏
45. Polarization of light
46. Polarization of Light
47. Some Terms related to Polarization of Light • Polarized Light • Unpolarized Light • Plane Polarized Light • Plane of vibration • Polarising angle • Plane of Polarization • Double refraction • Optic axis • Principal plane • Principal section
48. Important Mathematical Problems Type 1: Electromagnetic Wave E = E0sin(x – ct) Equation to be used B = B0sin(x – ct) Relation between electric & magnetic field, Bo = 𝑬 𝒐 𝒄
49. Type 2: Light speed C = f𝜆 = 1 ∈0 𝜇0 Type 3: Light speed, wave length & RI a 𝜇b= 𝐶 𝑎 𝐶 𝑏 = 𝜆 𝑎 𝜆 𝑏 a 𝜇b= 𝜇 𝑏 𝜇 𝑎
50. Speed of light in water is 2.22X108 ms-1. wavelength of sodium light in vacuum is 5892 Å then determine wavelength of that light in water. Hints: 𝑪 𝟎 𝑪 𝒘 = 𝝀 𝟎 𝝀 𝒘
51. Path difference between two points of a wave is 5𝜆 2 then determine the phase difference. 𝝅 Type 4: Phase difference & path difference Hints: 𝛿 = 2𝜋 𝜆 𝑥 Phase difference between two points of a wave is 𝜋 2 then determine path difference. 𝝀 𝟒
52. Type 5: distance between central bright to nth fringe 𝒙 𝒏 = 𝒏𝑫𝝀 𝒅 Where, n = number of fringe D = distance between the slit & the screen 𝜆 = wavelength d = distance between two slits This equation may be used to determine distance from central max to any fringe, screen distance, wavelength, distance between two slits, no. of fringe Type 6: width of the bright fringe 𝚫𝒙 = 𝑫𝝀 𝟐𝒅
53. Mathematical problems • In a Young’s double slit experiment, distance between two slits is 0.4mm. At 1m distance a fringe is created where the distance between the central max to 12th bright fringe is 9.3mm. Determine the wavelength of the wave. [3100 Å] • In a Young’s double slit experiment, the separation between the slits is 0.10 m, the wavelength of light used is 500 nm and the interference pattern is observed on a screen 1.0m away. Find the separation between successive bright bands. 𝒙 = 𝑫𝝀 𝒅
54. • In a Young’s double slit experiment, fringe width is found is 0.4mm. Keeping the arrangement same if the experiment is done in water then what will be the fringe width? Refractive index of water is 𝟒 𝟑 • 𝝁 𝒘 = ∆𝒙 ∆𝒙/ where, ∆𝒙/ is the new fringe width
55. An interference spectra is formed in the screen at a distance of 1m from two slits having separation of 0.4 mm. If the wavelength of light is 500 Å then a) Find the distance between two successive bright bands and b) What is the distance between two successive dark bands. a) b) 2x
56. Find 2d A double slit experiment is performed with light of wavelength 589nm and he interference pattern is observed on a screen 100 cm away. The tenth bright fringe has its centre at a distance of 10 mm from the central maximum. Find the separation between the slits
57. Condition for bright point: a sin𝜽 = (𝟐𝒏 + 𝟏) 𝝀 𝟐 Type 4: Diffraction Condition for dark point: a sin𝜽 = 𝒏𝝀 These equations are used to determine width of the slit, number of fringe, diffraction angle and wavelength For grating constant: d sin𝜽 = 𝒂 + 𝒃 𝒔𝒊𝒏𝜽 = 𝒔𝒊𝒏𝜽 𝑵 = 𝒏𝝀 Where, N = 𝟏 𝒂+𝒃
58. In a Fraunhauffer class diffraction experiment due to a single slit a light of wavelength of 5600Å is used. Determine the angle of diffraction for the first dark band. [width of the slit = 0.2 mm] We know, a sinθ = nλ Ans: 0.160
59. In a Fraunhauffer class diffraction light of wavelength of 5600Å is used. Find the angle of diffraction of the second maxima a sinθ = nλ θ = 300
60. A light of wavelength of 8X10-7 m incident on a plane grating produces the angle of diffraction of 300 for the first order. What is the number of lines per cm in the grating?
61. There are 4200 lines per cm in a grating. If parallel rays of sodium light are incident normally on it, then the second order spectral lines produces an angle of 300. Calculate the wavelength of sodium light We know, (a+b)Sinθn = nλ λ = 595 m
62. 1. In optics lab, Raihan incident a monochromatic light of 600 nm through a 2μm wide slit perpendicularly. H thought that he would see nine bright points. c) Determine angular distance between first order bright points. d) Analyze whether he could see nine bright points or not!
63. 2. In a Young’s double slit experiment distance between the slits is 0.3mm. Distance from the slit to the screen is 1m. While experimenting in air, distance between the central maxima to 8th bright fringe was found 6.2mm. The whole system is kept in water. c) Determine wavelength of light used in the experiment. d) In water, will there be any change in fringe width? Analyze.
64. 3. In Young’s double slit experiment following arrangement is shown. Wavelength of the light used 5800 Ǻ 1m 2mm 20cm c) Determine the wavelength of light used I the stem. d) If the screen distance is increased by 20 cm then will you get the fringe of same width? Analyze.
65. 1. Electromagnetic wave 2. Wave theory of light 3. Electromagnetic theory 4. Poynting vector 5. Wave front 6. Diffraction grating 7. Plane transmission grating 8. Grating constant 9. Polarized Light 10.Unpolarized Light 11.Plane Polarized Light 12.Plane of vibration 13.Polarising angle 14.Plane of Polarization 15.Double refraction 16.Optic axis 17.Principal plane 18.Principal section
66. 1. Compare 7 electromagnetic waves. 2. Write down the characteristics of electromagnetic waves. 3. What do you mean by 1 light year? 4. State Huygens’s principle of formation of wave front. 5. What is interference of light? Write down the conditions and characteristics of interference of light.
67. 6. Write down the difference between constructive and destructive interference. 7. What do you mean by coherent source? 8. Show relation between phase difference and path difference. 9. What is diffraction of light? Write down the condition for diffraction of light.
68. 10. Write down the difference between Fraunhoffer and Fresnel Class diffraction. 11. Write down the difference between Interference and diffraction. 12. Two same type of light source can’t produce interference – explain. 13. If a thin glass plate is placed on the path of one source then will there be any change in fringe? Explain your answer. 14. Longitudinal waves have no polarization – Explain.
69. 15. Light year through glass is 6.27X1012 km – What do you mean by this? 16. No source is coherent in nature – Explain.
70. Facts for MCQ 19. When the waves are coherent? 20. Conditions for interference of light. 21. When two coherent monochromatic light source forms constructive interference then phase difference becomes __________ 22. What is the reason for keeping two slits in case of Young’s double slit experiment? 23. Phase difference between the two points of a wave is 𝜋 2 then path difference between the point will be _______
71. Comparison between different Light Theory
72. Sl. No. Phenomena Corpuscular Wave EM wave Quantum Dual 1. Rectilinear Propagation √ √ √ √ √ 2. Reflection √ √ √ √ √ 3. Refraction √ √ √ √ √ 4. Dispersion X √ √ X √ 5. Interference X √ √ X √ 6. Diffraction X √ √ X √ 7. Polarization X √ √ X √ 8. Photoelectric effect X X X √ X