Diffraction Problems

This section provides 100 problems to test your understanding of diffraction of light, including calculations of minima positions, central maximum width, grating maxima angles, resolving power, and dispersion, as well as applications like X-ray diffraction and telescope resolution. Inspired by JEE Main, JEE Advanced, and NEET exam patterns, these problems are tailored for exam preparation, offering a mix of numerical, conceptual, and derivation-based challenges. NEET-style problems (66–100) are formatted as multiple-choice questions (MCQs) to match the exam’s objective format. Problems are organized by type to support progressive learning and build confidence in mastering wave optics, a key topic for JEE/NEET success.

Numerical Problems

1. A single slit of width $a=2\mu \text{m}$ is illuminated by light of wavelength $\lambda =500\text{nm}$. Calculate the angular position of the first minimum.

   • (a) ${14.4}^{\circ }$
   • (b) ${14.5}^{\circ }$
   • (c) ${14.6}^{\circ }$
   • (d) ${14.7}^{\circ }$

2. A single slit of width $a=1\mu \text{m}$ with $\lambda =600\text{nm}$ is viewed on a screen at $D=1\text{m}$. Calculate the width of the central maximum.

   • (a) $1.49\text{m}$
   • (b) $1.50\text{m}$
   • (c) $1.51\text{m}$
   • (d) $1.52\text{m}$

3. A diffraction grating with $d=2\mu \text{m}$ is illuminated by $\lambda =500\text{nm}$. Calculate the angular position of the first-order maximum.

   • (a) ${14.4}^{\circ }$
   • (b) ${14.5}^{\circ }$
   • (c) ${14.6}^{\circ }$
   • (d) ${14.7}^{\circ }$

4. A single slit of width $a=5\mu \text{m}$ with $\lambda =500\text{nm}$. Calculate the angular position of the second minimum.

   • (a) ${11.4}^{\circ }$
   • (b) ${11.5}^{\circ }$
   • (c) ${11.6}^{\circ }$
   • (d) ${11.7}^{\circ }$

5. A diffraction grating with 500 lines/mm is illuminated by $\lambda =600\text{nm}$. Calculate the angular separation between the first and second-order maxima.

   • (a) ${19.3}^{\circ }$
   • (b) ${19.4}^{\circ }$
   • (c) ${19.5}^{\circ }$
   • (d) ${19.6}^{\circ }$

6. A telescope with aperture $a=0.05\text{m}$ uses $\lambda =550\text{nm}$. Calculate the minimum angular separation ${\theta }_{\text{min}}$.

   • (a) $1.34\times {10}^{-5}\text{rad}$
   • (b) $1.34\times {10}^{-5}\text{rad}$
   • (c) $1.35\times {10}^{-5}\text{rad}$
   • (d) $1.36\times {10}^{-5}\text{rad}$

7. X-rays with $\lambda =0.15\text{nm}$ are diffracted by a crystal with $d=0.2\text{nm}$, $m=1$. Calculate the diffraction angle $\theta$.

   • (a) ${21.9}^{\circ }$
   • (b) ${22.0}^{\circ }$
   • (c) ${22.1}^{\circ }$
   • (d) ${22.2}^{\circ }$

8. A single slit with $a=3\mu \text{m}$, $\lambda =600\text{nm}$, $D=2\text{m}$. Calculate the width of the central maximum.

   • (a) $0.79\text{m}$
   • (b) $0.80\text{m}$
   • (c) $0.81\text{m}$
   • (d) $0.82\text{m}$

9. A diffraction grating with $d=1.5\mu \text{m}$, $\lambda =400\text{nm}$. Calculate ${\theta }_2$.

   • (a) ${32.4}^{\circ }$
   • (b) ${32.5}^{\circ }$
   • (c) ${32.6}^{\circ }$
   • (d) ${32.7}^{\circ }$

10. A microscope with $a=0.02\text{m}$, $\lambda =450\text{nm}$. Calculate ${\theta }_{\text{min}}$.

    • (a) $2.74\times {10}^{-5}\text{rad}$
    • (b) $2.75\times {10}^{-5}\text{rad}$
    • (c) $2.76\times {10}^{-5}\text{rad}$
    • (d) $2.77\times {10}^{-5}\text{rad}$

11. A single slit with $a=4\mu \text{m}$, $\lambda =500\text{nm}$. Calculate the angular position of the third minimum.

    • (a) ${21.9}^{\circ }$
    • (b) ${22.0}^{\circ }$
    • (c) ${22.1}^{\circ }$
    • (d) ${22.2}^{\circ }$

12. A diffraction grating with 600 lines/mm, $\lambda =500\text{nm}$. Calculate ${\theta }_1$.

    • (a) ${17.4}^{\circ }$
    • (b) ${17.5}^{\circ }$
    • (c) ${17.6}^{\circ }$
    • (d) ${17.7}^{\circ }$

13. X-rays with $\lambda =0.1\text{nm}$, $d=0.3\text{nm}$, $m=2$. Calculate $\theta$.

    • (a) ${19.4}^{\circ }$
    • (b) ${19.5}^{\circ }$
    • (c) ${19.6}^{\circ }$
    • (d) ${19.7}^{\circ }$

14. A single slit with $a=1.5\mu \text{m}$, $\lambda =600\text{nm}$, $D=1.5\text{m}$. Calculate the width of the central maximum.

    • (a) $1.19\text{m}$
    • (b) $1.20\text{m}$
    • (c) $1.21\text{m}$
    • (d) $1.22\text{m}$

15. A diffraction grating with $d=2\mu \text{m}$, $N=1000$, $\lambda =500\text{nm}$. Calculate the resolving power for $m=1$.

    • (a) 999
    • (b) 1000
    • (c) 1001
    • (d) 1002

16. A single slit with $a=2.5\mu \text{m}$, $\lambda =500\text{nm}$. Calculate the angular position of the first minimum.

    • (a) ${11.4}^{\circ }$
    • (b) ${11.5}^{\circ }$
    • (c) ${11.6}^{\circ }$
    • (d) ${11.7}^{\circ }$

17. A diffraction grating with $d=3\mu \text{m}$, $\lambda =600\text{nm}$. Calculate the angular dispersion $\frac{d\theta }{d\lambda }$ for $m=1$ at $\theta ={11.5}^{\circ }$.

    • (a) $0.33\text{rad}/\mu \text{m}$
    • (b) $0.34\text{rad}/\mu \text{m}$
    • (c) $0.35\text{rad}/\mu \text{m}$
    • (d) $0.36\text{rad}/\mu \text{m}$

18. A telescope with $a=0.1\text{m}$, $\lambda =550\text{nm}$. Calculate ${\theta }_{\text{min}}$.

    • (a) $6.70\times {10}^{-6}\text{rad}$
    • (b) $6.71\times {10}^{-6}\text{rad}$
    • (c) $6.72\times {10}^{-6}\text{rad}$
    • (d) $6.73\times {10}^{-6}\text{rad}$

19. X-rays with $\lambda =0.12\text{nm}$, $d=0.25\text{nm}$, $m=1$. Calculate $\theta$.

    • (a) ${28.6}^{\circ }$
    • (b) ${28.7}^{\circ }$
    • (c) ${28.8}^{\circ }$
    • (d) ${28.9}^{\circ }$

20. A single slit with $a=10\mu \text{m}$, $\lambda =500\text{nm}$, $D=2\text{m}$. Calculate the width of the central maximum.

    • (a) $0.19\text{m}$
    • (b) $0.20\text{m}$
    • (c) $0.21\text{m}$
    • (d) $0.22\text{m}$

21. A diffraction grating with $d=1.8\mu \text{m}$, $\lambda =450\text{nm}$. Calculate ${\theta }_1$.

    • (a) ${14.4}^{\circ }$
    • (b) ${14.5}^{\circ }$
    • (c) ${14.6}^{\circ }$
    • (d) ${14.7}^{\circ }$

22. A single slit with $a=1\mu \text{m}$, $\lambda =400\text{nm}$. Calculate the angular position of the first minimum.

    • (a) ${23.4}^{\circ }$
    • (b) ${23.5}^{\circ }$
    • (c) ${23.6}^{\circ }$
    • (d) ${23.7}^{\circ }$

23. A diffraction grating with $N=1500$, $d=2.5\mu \text{m}$, $\lambda =500\text{nm}$. Calculate the resolving power for $m=2$.

    • (a) 2999
    • (b) 3000
    • (c) 3001
    • (d) 3002

24. X-rays with $\lambda =0.18\text{nm}$, $d=0.4\text{nm}$, $m=2$. Calculate $\theta$.

    • (a) ${26.5}^{\circ }$
    • (b) ${26.6}^{\circ }$
    • (c) ${26.7}^{\circ }$
    • (d) ${26.8}^{\circ }$

25. A single slit with $a=2\mu \text{m}$, $\lambda =600\text{nm}$, $D=1\text{m}$. Calculate the width of the central maximum.

    • (a) $0.59\text{m}$
    • (b) $0.60\text{m}$
    • (c) $0.61\text{m}$
    • (d) $0.62\text{m}$

26. A diffraction grating with 400 lines/mm, $\lambda =550\text{nm}$. Calculate ${\theta }_1$.

    • (a) ${12.6}^{\circ }$
    • (b) ${12.7}^{\circ }$
    • (c) ${12.8}^{\circ }$
    • (d) ${12.9}^{\circ }$

27. A telescope with $a=0.03\text{m}$, $\lambda =500\text{nm}$. Calculate ${\theta }_{\text{min}}$.

    • (a) $2.03\times {10}^{-5}\text{rad}$
    • (b) $2.04\times {10}^{-5}\text{rad}$
    • (c) $2.05\times {10}^{-5}\text{rad}$
    • (d) $2.06\times {10}^{-5}\text{rad}$

28. A single slit with $a=6\mu \text{m}$, $\lambda =600\text{nm}$. Calculate the angular position of the second minimum.

    • (a) ${11.4}^{\circ }$
    • (b) ${11.5}^{\circ }$
    • (c) ${11.6}^{\circ }$
    • (d) ${11.7}^{\circ }$

29. A diffraction grating with $d=2\mu \text{m}$, $\lambda =500\text{nm}$. Calculate the angular separation between the second and third orders.

    • (a) ${9.6}^{\circ }$
    • (b) ${9.7}^{\circ }$
    • (c) ${9.8}^{\circ }$
    • (d) ${9.9}^{\circ }$

30. X-rays with $\lambda =0.14\text{nm}$, $d=0.35\text{nm}$, $m=1$. Calculate $\theta$.

    • (a) ${23.4}^{\circ }$
    • (b) ${23.5}^{\circ }$
    • (c) ${23.6}^{\circ }$
    • (d) ${23.7}^{\circ }$

31. A spacecraft optical system uses a single slit with $a=1.2\mu \text{m}$, $\lambda =600\text{nm}$, $D=2\text{m}$. Calculate the width of the central maximum.

    • (a) $1.99\text{m}$
    • (b) $2.00\text{m}$
    • (c) $2.01\text{m}$
    • (d) $2.02\text{m}$

32. A diffraction grating with $d=1.6\mu \text{m}$, $N=1200$, $\lambda =500\text{nm}$. Calculate the resolving power for $m=1$.

    • (a) 1199
    • (b) 1200
    • (c) 1201
    • (d) 1202

33. A single slit with $a=1.8\mu \text{m}$, $\lambda =450\text{nm}$. Calculate the angular position of the first minimum.

    • (a) ${14.4}^{\circ }$
    • (b) ${14.5}^{\circ }$
    • (c) ${14.6}^{\circ }$
    • (d) ${14.7}^{\circ }$

34. A diffraction grating with 700 lines/mm, $\lambda =500\text{nm}$. Calculate ${\theta }_2$.

    • (a) ${44.4}^{\circ }$
    • (b) ${44.5}^{\circ }$
    • (c) ${44.6}^{\circ }$
    • (d) ${44.7}^{\circ }$

35. A microscope with $a=0.01\text{m}$, $\lambda =400\text{nm}$. Calculate ${\theta }_{\text{min}}$.

    • (a) $4.87\times {10}^{-5}\text{rad}$
    • (b) $4.88\times {10}^{-5}\text{rad}$
    • (c) $4.89\times {10}^{-5}\text{rad}$
    • (d) $4.90\times {10}^{-5}\text{rad}$

---

Conceptual Problems

36. What does Huygens' principle state about wave propagation?

• (a) Waves travel in straight lines only
• (b) Each point on a wavefront acts as a source of secondary wavelets
• (c) Waves cannot bend around obstacles
• (d) Waves must be incoherent

37. What type of diffraction occurs when the screen is far from the slit?

• (a) Fresnel diffraction
• (b) Fraunhofer diffraction
• (c) No diffraction
• (d) Partial diffraction

38. What is the unit of angular position $\theta$ in SI units?

• (a) Meter
• (b) Radian
• (c) Watt
• (d) Hertz

39. What happens at the first minimum in single-slit diffraction?

• (a) Maximum intensity
• (b) Zero intensity
• (c) No diffraction
• (d) Partial intensity

40. What does the condition $d\sin \theta =m\lambda$ represent in a diffraction grating?

• (a) Position of minima
• (b) Position of principal maxima
• (c) Central maximum width
• (d) Intensity distribution

41. What is the unit of resolving power $R$?

• (a) Radian
• (b) Meter
• (c) Dimensionless
• (d) Watt

42. What does a smaller ${\theta }_{\text{min}}$ indicate for an optical instrument?

• (a) Lower resolution
• (b) Higher resolution
• (c) No resolution
• (d) Partial resolution

43. What happens to the width of the central maximum if the slit width $a$ increases?

• (a) Increases
• (b) Decreases
• (c) Remains the same
• (d) Becomes zero

44. What does X-ray diffraction help determine?

• (a) Wavelength of light
• (b) Crystal structure
• (c) Intensity of light
• (d) Phase difference

45. What is the dimension of angular dispersion $\frac{d\theta }{d\lambda }$?

• (a) $[{\text{L}}^{-1}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

46. What does a central maximum in single-slit diffraction indicate?

• (a) Zero intensity
• (b) Maximum intensity
• (c) No diffraction
• (d) Partial diffraction

47. What is the significance of $1.22\frac{\lambda }{a}$?

• (a) Path difference
• (b) Minimum angular separation for resolution
• (c) Fringe spacing
• (d) Intensity distribution

48. What happens to the diffraction pattern if the wavelength $\lambda$ increases?

• (a) Pattern narrows
• (b) Pattern widens
• (c) Pattern remains the same
• (d) Pattern disappears

49. What does holography rely on to reconstruct images?

• (a) Diffraction patterns
• (b) Refraction
• (c) Reflection
• (d) Absorption

50. How does diffraction assist in spacecraft optical systems?

• (a) Increases intensity
• (b) Enables precise resolution and spectral analysis
• (c) Reduces wavelength
• (d) Increases path difference

---

Derivation Problems

51. Derive the position of minima in single-slit diffraction $a\sin \theta =m\lambda$.

52. Derive the width of the central maximum in single-slit diffraction $w\approx 2D\frac{\lambda }{a}$.

53. Derive the intensity distribution in single-slit diffraction $I=I_0{\left(\frac{\sin \alpha }{\alpha }\right)}^2$.

54. Derive the position of principal maxima in a diffraction grating $d\sin \theta =m\lambda$.

55. Derive Bragg’s law for X-ray diffraction $2d\sin \theta =m\lambda$.

56. Derive the resolving power of a diffraction grating $R=mN$.

57. Derive the angular dispersion of a diffraction grating $\frac{d\theta }{d\lambda }=\frac{m}{d\cos \theta }$.

58. Derive the minimum angular separation for a circular aperture ${\theta }_{\text{min}}=1.22\frac{\lambda }{a}$.

59. Derive the angular position of the first minimum in single-slit diffraction $\sin {\theta }_1=\frac{\lambda }{a}$.

60. Derive the intensity at the central maximum in single-slit diffraction.

61. Derive the path difference in single-slit diffraction leading to minima.

62. Derive the resolving power of a telescope using diffraction.

63. Derive the angular separation between consecutive orders in a diffraction grating.

64. Derive the width of the central maximum if the wavelength changes in single-slit diffraction.

65. Derive the diffraction angle for X-ray diffraction given $d$ and $\lambda$.

---

NEET-style Conceptual Problems

66. What is the unit of wavelength $\lambda$ in SI units?

• (a) Meter
• (b) Radian
• (c) Hertz
• (d) Watt

67. What does a larger slit width $a$ do to the diffraction pattern?

• (a) Widens the pattern
• (b) Narrows the pattern
• (c) No effect
• (d) Eliminates the pattern

68. What is the relationship between ${\theta }_{\text{min}}$ and wavelength $\lambda$ in resolving power?

• (a) ${\theta }_{\text{min}}\propto \frac{1}{\lambda }$
• (b) ${\theta }_{\text{min}}\propto \lambda$
• (c) ${\theta }_{\text{min}}$ is independent of $\lambda$
• (d) ${\theta }_{\text{min}}\propto {\lambda }^2$

69. What happens to the diffraction pattern if the screen distance $D$ increases?

• (a) Pattern narrows
• (b) Pattern widens
• (c) Pattern remains the same
• (d) Pattern disappears

70. What is the dimension of $\sin \theta$ in diffraction equations?

• (a) Dimensionless
• (b) $[\text{L}{\text{T}}^{-1}]$
• (c) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (d) $[\text{L}{\text{T}}^{-2}]$

71. What does Huygens' principle explain in diffraction?

• (a) Straight-line propagation only
• (b) Bending of light around obstacles
• (c) Reflection of light
• (d) Refraction of light

72. What is the role of diffraction in a telescope?

• (a) Increases intensity
• (b) Limits resolution through ${\theta }_{\text{min}}$
• (c) Reduces wavelength
• (d) Increases path difference

73. What happens to the resolving power of a grating if $N$ increases?

• (a) Decreases
• (b) Increases
• (c) Remains the same
• (d) Becomes zero

74. Why does X-ray diffraction use small wavelengths?

• (a) To increase intensity
• (b) To match the scale of atomic lattices
• (c) To reduce resolution
• (d) To increase path difference

75. What is the unit of intensity $I$?

• (a) W/m²
• (b) Radian
• (c) Hertz
• (d) Meter

76. What does a zero intensity in single-slit diffraction indicate?

• (a) Central maximum
• (b) Minimum position
• (c) No diffraction
• (d) Partial diffraction

77. Which type of diffraction is used in a spectrometer?

• (a) Fresnel diffraction
• (b) Fraunhofer diffraction
• (c) No diffraction
• (d) Partial diffraction

78. What is the orientation of diffraction patterns in a grating?

• (a) Circular
• (b) Linear maxima
• (c) Random
• (d) No pattern

79. What does a pseudo-force do in a non-inertial frame for diffraction calculations?

• (a) Affects perceived diffraction angle
• (b) Affects intensity
• (c) Creates diffraction
• (d) Reduces wavelength

80. What is the dimension of $a\sin \theta$?

• (a) $[\text{L}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

81. What is the role of diffraction in spacecraft spectroscopy?

• (a) Increases intensity
• (b) Enables spectral analysis through gratings
• (c) Reduces wavelength
• (d) Increases path difference

82. What happens to the central maximum width if $\lambda$ decreases?

• (a) Increases
• (b) Decreases
• (c) Remains the same
• (d) Becomes zero

83. Why does a diffraction grating produce sharp maxima?

• (a) Due to multiple slit interference
• (b) Due to refraction
• (c) Due to reflection
• (d) Due to absorption

84. What is the significance of $2d\sin \theta$?

• (a) Intensity in single-slit diffraction
• (b) Path difference in X-ray diffraction
• (c) Fringe spacing
• (d) Phase difference

85. What is the unit of slit width $a$?

• (a) Meter
• (b) Radian
• (c) Hertz
• (d) Watt

86. What does a high resolving power in a grating indicate?

• (a) Lower resolution
• (b) Higher resolution
• (c) No resolution
• (d) Partial resolution

87. What is the physical significance of $\frac{\sin \alpha }{\alpha }$?

• (a) Path difference
• (b) Intensity factor in single-slit diffraction
• (c) Fringe spacing
• (d) Wavelength

88. Why does diffraction occur when slit width $a\approx \lambda$?

• (a) Due to $a\sin \theta =m\lambda$
• (b) Due to wave bending being significant
• (c) Due to reflection
• (d) Due to refraction

89. What is the dimension of $\frac{\lambda }{a}$?

• (a) Dimensionless
• (b) $[\text{L}{\text{T}}^{-1}]$
• (c) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (d) $[\text{L}{\text{T}}^{-2}]$

90. How does diffraction assist in optical data storage?

• (a) Increases intensity
• (b) Uses diffraction patterns to read data
• (c) Reduces wavelength
• (d) Increases path difference

91. What is the role of aperture size $a$ in resolving power?

• (a) Determines the wavelength
• (b) Determines ${\theta }_{\text{min}}$
• (c) Determines intensity
• (d) Determines phase difference

92. What does a wide central maximum in single-slit diffraction indicate?

• (a) Large $a$
• (b) Small $a$
• (c) No diffraction
• (d) Partial diffraction

93. What is the physical significance of $mN$?

• (a) Path difference
• (b) Resolving power of a diffraction grating
• (c) Fringe spacing
• (d) Intensity

94. What is the dimension of $1.22\frac{\lambda }{a}$?

• (a) Radian
• (b) $[\text{L}{\text{T}}^{-1}]$
• (c) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (d) $[\text{L}{\text{T}}^{-2}]$

95. Why does the diffraction pattern in single-slit diffraction depend on $\lambda$?

• (a) Due to $a\sin \theta =m\lambda$
• (b) Due to intensity
• (c) Due to phase difference
• (d) Due to coherence

---

NEET-style Numerical Problems

96. A single slit with $a=2\mu \text{m}$, $\lambda =400\text{nm}$. Calculate the angular position of the first minimum.

• (a) ${11.4}^{\circ }$
• (b) ${11.5}^{\circ }$
• (c) ${11.6}^{\circ }$
• (d) ${11.7}^{\circ }$

97. A diffraction grating with $d=2.5\mu \text{m}$, $\lambda =500\text{nm}$. Calculate ${\theta }_1$.

• (a) ${11.4}^{\circ }$
• (b) ${11.5}^{\circ }$
• (c) ${11.6}^{\circ }$
• (d) ${11.7}^{\circ }$

98. A telescope with $a=0.04\text{m}$, $\lambda =500\text{nm}$. Calculate ${\theta }_{\text{min}}$.

• (a) $1.52\times {10}^{-5}\text{rad}$
• (b) $1.53\times {10}^{-5}\text{rad}$
• (c) $1.54\times {10}^{-5}\text{rad}$
• (d) $1.55\times {10}^{-5}\text{rad}$

99. X-rays with $\lambda =0.16\text{nm}$, $d=0.32\text{nm}$, $m=1$. Calculate $\theta$.

• (a) ${29.9}^{\circ }$
• (b) ${30.0}^{\circ }$
• (c) ${30.1}^{\circ }$
• (d) ${30.2}^{\circ }$

100. A single slit with $a=1.5\mu \text{m}$, $\lambda =600\text{nm}$, $D=1\text{m}$. Calculate the width of the central maximum.
     - (a) $1.19\text{m}$
     - (b) $1.20\text{m}$
     - (c) $1.21\text{m}$
     - (d) $1.22\text{m}$

Back to Chapter

Return to Diffraction Chapter