Images Problems

This section provides 100 problems to test your understanding of image formation through geometric optics, including calculations of image distance, magnification, and focal length for mirrors and lenses, as well as the principles of optical instruments like microscopes and telescopes. 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 ray optics, a key topic for JEE/NEET success.

Numerical Problems

1. An object is placed 20 cm in front of a plane mirror. Calculate the distance of the image from the mirror.

   • (a) 19.9 cm
   • (b) 20.0 cm
   • (c) 20.1 cm
   • (d) 20.2 cm

2. A concave mirror has a focal length of 15 cm. An object is placed 25 cm in front of it. Calculate the image distance $v$.

   • (a) 37.4 cm
   • (b) 37.5 cm
   • (c) 37.6 cm
   • (d) 37.7 cm

3. A convex mirror has a focal length of 10 cm. An object is placed 30 cm in front of it. Calculate the image distance $v$.

   • (a) -7.4 cm
   • (b) -7.5 cm
   • (c) -7.6 cm
   • (d) -7.7 cm

4. A concave mirror with $f=20$ cm forms an image 40 cm in front of it. Calculate the object distance $u$.

   • (a) -39.9 cm
   • (b) -40.0 cm
   • (c) -40.1 cm
   • (d) -40.2 cm

5. A convex lens has a focal length of 25 cm. An object is placed 50 cm in front of it. Calculate the image distance $v$.

   • (a) 49.9 cm
   • (b) 50.0 cm
   • (c) 50.1 cm
   • (d) 50.2 cm

6. A concave lens has a focal length of 15 cm. An object is placed 20 cm in front of it. Calculate the image distance $v$.

   • (a) -8.5 cm
   • (b) -8.6 cm
   • (c) -8.7 cm
   • (d) -8.8 cm

7. A convex lens with $f=10$ cm forms an image 30 cm behind it. Calculate the object distance $u$.

   • (a) -14.9 cm
   • (b) -15.0 cm
   • (c) -15.1 cm
   • (d) -15.2 cm

8. A concave mirror has $f=12$ cm, and an object is at 18 cm. Calculate the magnification $m$.

   • (a) -1.99
   • (b) -2.00
   • (c) -2.01
   • (d) -2.02

9. A convex lens with $f=20$ cm has an object at 40 cm. Calculate the magnification $m$.

   • (a) -0.99
   • (b) -1.00
   • (c) -1.01
   • (d) -1.02

10. A microscope has an objective lens with $f_o=2$ cm and an eyepiece with $f_e=5$ cm. The tube length is 20 cm, and the near point is 25 cm. Calculate the total magnification $M$.

    • (a) 49.9
    • (b) 50.0
    • (c) 50.1
    • (d) 50.2

11. A telescope has an objective lens with $f_o=100$ cm and an eyepiece with $f_e=4$ cm. Calculate the magnification $M$.

    • (a) -24.9
    • (b) -25.0
    • (c) -25.1
    • (d) -25.2

12. A human eye has a near point of 25 cm. An object is placed 10 cm in front of it. Calculate the magnification $M$ (image at near point).

    • (a) 2.49
    • (b) 2.50
    • (c) 2.51
    • (d) 2.52

13. A convex lens has $n=1.5$, $R_1=30$ cm, $R_2=-40$ cm. Calculate the focal length $f$.

    • (a) 47.9 cm
    • (b) 48.0 cm
    • (c) 48.1 cm
    • (d) 48.2 cm

14. A concave mirror has $f=10$ cm, and an object is at 30 cm. Calculate the image distance $v$.

    • (a) 14.9 cm
    • (b) 15.0 cm
    • (c) 15.1 cm
    • (d) 15.2 cm

15. A convex mirror has $f=20$ cm, and an object is at 40 cm. Calculate $v$.

    • (a) -13.2 cm
    • (b) -13.3 cm
    • (c) -13.4 cm
    • (d) -13.5 cm

16. A convex lens with $f=30$ cm has an object at 15 cm. Calculate $v$.

    • (a) -29.9 cm
    • (b) -30.0 cm
    • (c) -30.1 cm
    • (d) -30.2 cm

17. A concave lens with $f=20$ cm has an object at 40 cm. Calculate $v$.

    • (a) -13.2 cm
    • (b) -13.3 cm
    • (c) -13.4 cm
    • (d) -13.5 cm

18. A concave mirror with $u=20$ cm forms an image with $m=-2$. Calculate $v$.

    • (a) 39.9 cm
    • (b) 40.0 cm
    • (c) 40.1 cm
    • (d) 40.2 cm

19. A convex lens with $u=60$ cm has $m=-0.5$. Calculate $v$.

    • (a) -29.9 cm
    • (b) -30.0 cm
    • (c) -30.1 cm
    • (d) -30.2 cm

20. A telescope has $f_o=150$ cm, $f_e=5$ cm. Calculate the length of the telescope in normal adjustment.

    • (a) 154.9 cm
    • (b) 155.0 cm
    • (c) 155.1 cm
    • (d) 155.2 cm

21. A microscope has $f_o=1.5$ cm, $f_e=6$ cm, $L=18$ cm, $D=25$ cm. Calculate $M$.

    • (a) 49.9
    • (b) 50.0
    • (c) 50.1
    • (d) 50.2

22. A human eye has a near point of 20 cm. An object is at 8 cm. Calculate $M$.

    • (a) 2.49
    • (b) 2.50
    • (c) 2.51
    • (d) 2.52

23. A convex lens has $n=1.6$, $R_1=25$ cm, $R_2=-25$ cm. Calculate $f$.

    • (a) 20.7 cm
    • (b) 20.8 cm
    • (c) 20.9 cm
    • (d) 21.0 cm

24. A concave mirror has $f=8$ cm, object at 12 cm. Calculate $m$.

    • (a) -1.99
    • (b) -2.00
    • (c) -2.01
    • (d) -2.02

25. A convex lens with $f=15$ cm has an object at 30 cm. Calculate $m$.

    • (a) -0.99
    • (b) -1.00
    • (c) -1.01
    • (d) -1.02

26. A convex mirror with $f=25$ cm has an object at 50 cm. Calculate $v$.

    • (a) -16.6 cm
    • (b) -16.7 cm
    • (c) -16.8 cm
    • (d) -16.9 cm

27. A concave lens with $f=10$ cm has an object at 15 cm. Calculate $v$.

    • (a) -5.9 cm
    • (b) -6.0 cm
    • (c) -6.1 cm
    • (d) -6.2 cm

28. A concave mirror with $u=15$ cm has $m=-3$. Calculate $v$.

    • (a) 44.9 cm
    • (b) 45.0 cm
    • (c) 45.1 cm
    • (d) 45.2 cm

29. A convex lens with $u=20$ cm has $m=2$. Calculate $v$.

    • (a) 39.9 cm
    • (b) 40.0 cm
    • (c) 40.1 cm
    • (d) 40.2 cm

30. A telescope has $f_o=80$ cm, $f_e=2$ cm. Calculate $M$.

    • (a) -39.9
    • (b) -40.0
    • (c) -40.1
    • (d) -40.2

31. A spacecraft uses a convex lens with $f=0.2$ m for navigation imaging. An object is at 0.5 m. Calculate $v$.

    • (a) 0.332 m
    • (b) 0.333 m
    • (c) 0.334 m
    • (d) 0.335 m

32. A microscope has $f_o=1$ cm, $f_e=4$ cm, $L=16$ cm, $D=25$ cm. Calculate $M$.

    • (a) 99.9
    • (b) 100.0
    • (c) 100.1
    • (d) 100.2

33. A human eye has a near point of 30 cm. An object is at 12 cm. Calculate $M$.

    • (a) 2.49
    • (b) 2.50
    • (c) 2.51
    • (d) 2.52

34. A convex lens with $n=1.5$, $R_1=40$ cm, $R_2=-20$ cm. Calculate $f$.

    • (a) 26.6 cm
    • (b) 26.7 cm
    • (c) 26.8 cm
    • (d) 26.9 cm

35. A concave mirror with $f=18$ cm has an object at 36 cm. Calculate $v$.

    • (a) 35.9 cm
    • (b) 36.0 cm
    • (c) 36.1 cm
    • (d) 36.2 cm

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Conceptual Problems

36. What does the law of reflection state?

• (a) Angle of incidence equals angle of refraction
• (b) Angle of incidence equals angle of reflection
• (c) Incident ray is perpendicular to the reflected ray
• (d) Reflected ray is parallel to the normal

37. What type of image does a plane mirror always form?

• (a) Real and inverted
• (b) Virtual and upright
• (c) Real and upright
• (d) Virtual and inverted

38. What is the unit of focal length in SI units?

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

39. What happens to the image formed by a convex mirror?

• (a) Always real and inverted
• (b) Always virtual and upright
• (c) Always real and upright
• (d) Always virtual and inverted

40. What does Snell’s law describe?

• (a) Reflection at a mirror
• (b) Refraction at an interface
• (c) Diffraction of light
• (d) Interference of light

41. What is the unit of magnification $m$?

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

42. What does a negative magnification indicate for a mirror?

• (a) Upright image
• (b) Inverted image
• (c) Virtual image
• (d) No image

43. What happens to the image formed by a concave lens?

• (a) Always real and inverted
• (b) Always virtual and upright
• (c) Always real and upright
• (d) Always virtual and inverted

44. What does the magnification of a telescope depend on?

• (a) Focal length of the objective only
• (b) Focal length of the eyepiece only
• (c) Ratio of focal lengths of objective and eyepiece
• (d) Distance between the lenses

45. What is the dimension of refractive index $n$?

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

46. What does a positive image distance $v$ indicate for a convex lens?

• (a) Virtual image
• (b) Real image
• (c) No image
• (d) Inverted image

47. What is the significance of $(n-1)$ in the lensmaker’s formula?

• (a) Magnification of the lens
• (b) Refractive index difference
• (c) Focal length of the lens
• (d) Image distance

48. What does the near point of the human eye represent?

• (a) Farthest distance for clear vision
• (b) Closest distance for clear vision
• (c) Focal length of the eye
• (d) Magnification of the eye

49. What does a negative focal length indicate for a lens?

• (a) Converging lens
• (b) Diverging lens
• (c) Plane lens
• (d) No lens

50. How do optical instruments assist in spacecraft navigation?

• (a) Increase magnification
• (b) Enable precise imaging of distant objects
• (c) Reduce focal length
• (d) Increase refractive index

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Derivation Problems

51. Derive the mirror formula for a concave mirror $\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$.

52. Derive the magnification formula for a mirror $m=-\frac{v}{u}$.

53. Derive Snell’s law $n_1\sin {\theta }_1=n_2\sin {\theta }_2$.

54. Derive the lens formula for a thin convex lens $\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$.

55. Derive the lensmaker’s formula $\frac{1}{f}=(n-1)(\frac{1}{R_1}-\frac{1}{R_2})$.

56. Derive the magnification formula for a lens $m=\frac{v}{u}$.

57. Derive the total magnification of a compound microscope $M\approx \frac{L}{f_o}\times \frac{D}{f_e}$.

58. Derive the magnification of an astronomical telescope $M=-\frac{f_o}{f_e}$.

59. Derive the focal length of a convex mirror using the mirror formula.

60. Derive the image distance for a plane mirror.

61. Derive the magnification of the human eye when the image is at the near point.

62. Derive the relationship between focal length and radius of curvature for a spherical mirror $f=\frac{R}{2}$.

63. Derive the image distance for a concave lens using the lens formula.

64. Derive the object distance given the image distance and magnification for a lens.

65. Derive the sign convention for a convex lens system.

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NEET-style Conceptual Problems

66. What is the unit of refractive index $n$ in SI units?

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

67. What does a plane mirror produce in terms of image orientation?

• (a) Inverted image
• (b) Upright image
• (c) No image
• (d) Distorted image

68. What is the relationship between focal length $f$ and radius of curvature $R$ for a spherical mirror?

• (a) $f=R$
• (b) $f=\frac{R}{2}$
• (c) $f=2R$
• (d) $f=\frac{R}{4}$

69. What happens to the image formed by a convex lens when the object is beyond $2f$?

• (a) Virtual and upright
• (b) Real and inverted
• (c) Virtual and inverted
• (d) Real and upright

70. What is the dimension of magnification $m$?

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

71. What does the lensmaker’s formula depend on?

• (a) Object distance
• (b) Image distance
• (c) Refractive index and radii of curvature
• (d) Magnification

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

• (a) Forms the primary image
• (b) Magnifies the primary image
• (c) Reduces the focal length
• (d) Increases the refractive index

73. What happens to the magnification of a microscope if $f_e$ decreases?

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

74. Why does the human eye adjust its focal length?

• (a) To change magnification
• (b) To accommodate for different distances
• (c) To reduce image size
• (d) To increase refractive index

75. What is the unit of power of a lens?

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

76. What does a virtual image indicate in terms of image distance $v$ for a lens?

• (a) $v$ is positive
• (b) $v$ is negative
• (c) $v$ is zero
• (d) $v$ is infinite

77. Which type of lens is used in a compound microscope’s objective?

• (a) Concave lens
• (b) Convex lens
• (c) Plane lens
• (d) No lens

78. What is the orientation of the image formed by an astronomical telescope?

• (a) Upright
• (b) Inverted
• (c) Random
• (d) No image

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

• (a) Affects perceived image position
• (b) Affects light intensity
• (c) Creates images
• (d) Reduces magnification

80. What is the dimension of focal length $f$?

• (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 lenses in spacecraft imaging systems?

• (a) Increase magnification
• (b) Form precise images of distant objects
• (c) Reduce focal length
• (d) Increase refractive index

82. What happens to the image distance $v$ if the object moves closer to a convex lens?

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

83. Why does a concave mirror form a real image when the object is beyond the focal point?

• (a) Due to convergence of reflected rays
• (b) Due to divergence of reflected rays
• (c) Due to static rays
• (d) Due to refraction

84. What is the significance of $\frac{v}{u}$ in lens magnification?

• (a) Focal length of the lens
• (b) Magnification of the lens
• (c) Refractive index
• (d) Image distance

85. What is the unit of object distance $u$?

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

86. What does a magnification of $m=1$ indicate for a lens?

• (a) Image is smaller than the object
• (b) Image is the same size as the object
• (c) Image is larger than the object
• (d) No image

87. What is the physical significance of $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$?

• (a) Snell’s law
• (b) Lens formula
• (c) Magnification formula
• (d) Lensmaker’s formula

88. Why does a convex lens form a virtual image when the object is inside the focal point?

• (a) Due to convergence of rays
• (b) Due to divergence of rays after refraction
• (c) Due to static rays
• (d) Due to reflection

89. What is the dimension of $\frac{1}{f}$?

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

90. How does the sign convention assist in spacecraft optical design?

• (a) Increases magnification
• (b) Ensures consistent image calculations
• (c) Reduces focal length
• (d) Increases refractive index

91. What is the role of the objective lens in a telescope?

• (a) Magnifies the image
• (b) Forms the primary image
• (c) Reduces magnification
• (d) Increases focal length

92. What does a high magnification in a microscope indicate?

• (a) Small image size
• (b) Large image size
• (c) No image
• (d) Real image

93. What is the physical significance of $(n-1)(\frac{1}{R_1}-\frac{1}{R_2})$?

• (a) Magnification of a lens
• (b) Focal length inverse of a lens
• (c) Image distance
• (d) Object distance

94. What is the dimension of $\sin \theta$ in Snell’s law?

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

95. Why does a plane mirror form an image at the same distance as the object?

• (a) Due to refraction
• (b) Due to laws of reflection
• (c) Due to diffraction
• (d) Due to interference

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NEET-style Numerical Problems

96. A concave mirror has $f=10$ cm, object at 20 cm. Calculate $v$.

• (a) 19.9 cm
• (b) 20.0 cm
• (c) 20.1 cm
• (d) 20.2 cm

97. A convex lens with $f=15$ cm has an object at 45 cm. Calculate $v$.

• (a) 22.4 cm
• (b) 22.5 cm
• (c) 22.6 cm
• (d) 22.7 cm

98. A convex mirror with $f=12$ cm has an object at 24 cm. Calculate $v$.

• (a) -7.9 cm
• (b) -8.0 cm
• (c) -8.1 cm
• (d) -8.2 cm

99. A telescope has $f_o=120$ cm, $f_e=6$ cm. Calculate $M$.

• (a) -19.9
• (b) -20.0
• (c) -20.1
• (d) -20.2

100. A convex lens with $n=1.5$, $R_1=30$ cm, $R_2=-30$ cm. Calculate $f$.
     - (a) 29.9 cm
     - (b) 30.0 cm
     - (c) 30.1 cm
     - (d) 30.2 cm

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