SECTION C: DETAILED SOLUTIONS
SIMPLEST LEVEL SOLUTIONS (1-15)
1. Answer: (c) Retina
The human eye forms a real, inverted image on the retina, which contains light-sensitive cells (rods and cones).
2. Answer: (b) Iris
The iris is the colored part of the eye that controls the size of the pupil and thus the amount of light entering the eye.
3. Answer: (c) Pupil
The pupil is the opening in the center of the iris through which light enters the eye.
4. Answer: (b) Cornea
The cornea is the transparent front layer of the eye that provides most of the eye's focusing power.
5. Answer: (b) Near-sightedness
Myopia or near-sightedness is a condition where distant objects appear blurred while near objects are seen clearly.
6. Answer: (b) Convex lens
Hypermetropia (far-sightedness) is corrected using a convex lens which converges light rays to bring the image forward onto the retina.
7. Answer: (c) Scattering
The sky appears blue due to Rayleigh scattering of sunlight by small particles in the atmosphere. Blue light is scattered more than other colors.
8. Answer: (b) Scattering
At sunset, sunlight travels through more atmosphere, and blue light is scattered away, leaving red light to reach our eyes.
9. Answer: (c) 25 cm
The minimum distance of distinct vision (near point) for a normal healthy eye is 25 cm.
10. Answer: (a) Old age
Presbyopia occurs with advancing age due to the gradual loss of flexibility of the eye lens.
11. Answer: (c) Iris
The iris controls the size of the pupil, thereby regulating the amount of light entering the eye.
12. Answer: (a) Atmospheric refraction
Stars twinkle due to atmospheric refraction caused by varying densities of air layers.
13. Answer: (c) Refraction and dispersion
Rainbow formation involves both refraction and dispersion of light through water droplets.
14. Answer: (a) Real and inverted
The eye lens forms a real, inverted image on the retina, but the brain interprets it as erect.
15. Answer: (c) Cylindrical lens
Astigmatism is corrected using cylindrical lenses which have different powers in different planes.
SIMPLE LEVEL SOLUTIONS (16-35)
16. Answer: (a) Accommodation
The ability of the eye to change its focal length by changing the curvature of the lens is called accommodation.
17. Answer: (b) Myopia
If a person cannot see beyond 2 m clearly, they have myopia (near-sightedness).
18. Answer: (a) Age
The power of accommodation decreases with age due to the hardening of the eye lens.
19. Answer: (d) Red
Red light has the maximum wavelength (≈700 nm) in the visible spectrum.
20. Answer: (c) Blue light
Scattering is inversely proportional to λ⁴, so blue light (shorter wavelength) is scattered most.
21. Answer: (c) Less than infinity
In myopia, the far point is at a finite distance, less than infinity.
22. Answer: (c) More than 25 cm
In hypermetropia, the near point is farther than the normal 25 cm.
23. Answer: (b) Atmospheric refraction
Both advanced sunrise and delayed sunset are due to atmospheric refraction bending light rays.
24. Answer: (b) Red is scattered least
Red light is scattered least, so it can travel farthest through fog and haze, making it ideal for danger signals.
25. Answer: (c) Presbyopia
Bifocal lenses correct presbyopia by providing different powers for near and distant vision.
26. Answer: (b) Changing lens curvature
Ciliary muscles change the curvature of the eye lens for accommodation.
27. Answer: (b) 1/16 second
Persistence of vision is about 1/16 second, which is the basis of motion pictures.
28. Answer: (c) Dispersion
Dispersion is the splitting of white light into its component colors due to different refractive indices.
29. Answer: (d) λ⁴
According to Rayleigh scattering law, scattered intensity ∝ 1/λ⁴.
30. Answer: (b) Near point
The least distance of distinct vision is called the near point of the eye.
31. Answer: (b) Varying air density
Atmospheric refraction occurs due to the gradual change in air density with altitude.
32. Answer: (a) Myopia
In myopia, distant objects appear blurred because the image forms in front of the retina.
33. Answer: (c) Iris
The iris functions like the diaphragm of a camera, controlling the amount of light entering.
34. Answer: (b) Variable with height
The refractive index of atmosphere varies with height due to changing air density.
35. Answer: (b) Red, Green, Blue
The three primary colors of light are Red, Green, and Blue (RGB).
EASY LEVEL SOLUTIONS (36-55)
36. Answer: (a) -1.25 D
For myopia correction: P = -1/f = -1/0.8 = -1.25 D (far point = 80 cm = 0.8 m)
37. Answer: (a) 0.5°
Both sun and moon subtend approximately 0.5° or 30 arc minutes at Earth.
38. Answer: (b) 48.6°
Critical angle C = sin⁻¹(1/μ) = sin⁻¹(1/(4/3)) = sin⁻¹(3/4) = 48.6°
39. Answer: (b) Positive
Hypermetropia requires converging (convex) lens with positive power.
40. Answer: (c) Color blindness
Color blindness is the inability to distinguish between certain colors, usually red and green.
41. Answer: (a) Mirage
Mirage is formed due to total internal reflection of light in layers of air with different densities.
42. Answer: (a) 525 nm
Wavelength in water = λ/μ = 700/(4/3) = 525 nm
43. Answer: (b) 20 cm
For myopia correction, the far point equals the focal length of the correcting lens = 20 cm.
44. Answer: (c) Stars are point sources
Stars twinkle because they appear as point sources, while planets have finite angular size.
45. Answer: (b) Refraction
Atmospheric refraction bends light rays, making the sun visible before actual sunrise.
46. Answer: (a) Less scattering
At noon, sunlight travels the shortest path through atmosphere, causing less scattering.
47. Answer: (c) 60 D to 64 D
Normal eye lens power varies from about 60 D (distant vision) to 64 D (near vision).
48. Answer: (a) Colors of rainbow
VIBGYOR represents the seven colors of rainbow: Violet, Indigo, Blue, Green, Yellow, Orange, Red.
49. Answer: (b) Surgery
Cataract (clouding of lens) is corrected by surgical replacement of the lens.
50. Answer: (c) 3 × 10⁸ m/s
Speed of light in vacuum is approximately 3 × 10⁸ m/s.
51. Answer: (b) Eyeball is too long
Myopia occurs when the eyeball is too long, causing images to form in front of the retina.
52. Answer: (c) 1/λ⁴
According to Rayleigh scattering, intensity of scattered light is proportional to 1/λ⁴.
53. Answer: (b) 50 cm
Focal length f = 1/P = 1/2 = 0.5 m = 50 cm
54. Answer: (a) Refraction
Atmospheric refraction causes the sun to appear flattened at the horizon.
55. Answer: (b) 2.3 cm
The image distance from lens to retina in normal eye is approximately 2.3 cm.
MODERATE LEVEL SOLUTIONS (56-75)
56. Answer: (c) 0 D, -1.25 D
For reading: Normal vision at 25 cm, so 0 D needed.
For distance: Myopia with far point 80 cm, so P = -1/0.8 = -1.25 D
57. Answer: (a) -0.5 D
Power = -1/far point = -1/2 = -0.5 D
58. Answer: (c) Refractive indices
Critical angle depends on the ratio of refractive indices: sin C = n₂/n₁
59. Answer: (a) +1.5 D
P = 1/0.25 - 1/0.40 = 4 - 2.5 = +1.5 D
60. Answer: (c) 5:1
Scattering ∝ 1/λ⁴. λ_blue/λ_red ≈ 450/700, so ratio ≈ (700/450)⁴ ≈ 5:1
61. Answer: (d) Black
Without atmosphere, there would be no scattering, so the sky would appear black like in space.
62. Answer: (a) 40 D
The cornea provides about 40 D of the eye's total refractive power.
63. Answer: (a) +1.5 D, -0.5 D
For reading: P = 1/0.25 - 1/0.40 = +1.5 D
For distance: P = -1/2 = -0.5 D
64. Answer: (a) 1.39 × 10⁹ m
Angular diameter = 32' = 32/60 degrees
Linear diameter = distance × angle(in radians) = 1.5 × 10¹¹ × (32/60) × (π/180) ≈ 1.39 × 10⁹ m
65. Answer: (a) Stars to appear higher
Atmospheric refraction bends light toward normal, making celestial objects appear higher than actual position.
66. Answer: (a) 400-700 nm
Visible light wavelength range is approximately 400 nm (violet) to 700 nm (red).
67. Answer: (b) 25 cm
If accommodation = 4 D, then 1/near point = 1/∞ + 4 = 4
Near point = 1/4 = 0.25 m = 25 cm
68. Answer: (b) Total internal reflection
Mirage is formed due to total internal reflection in hot air layers near the ground.
69. Answer: (a) f₀ + fₑ
In normal adjustment of telescope, separation = f₀ + fₑ (focal lengths of objective and eyepiece).
70. Answer: (b) 50 cm
Power = -2 D, so far point = 1/2 = 0.5 m = 50 cm
71. Answer: (a) 1.36 to 1.40
The refractive index of eye lens varies from 1.36 to 1.40 during accommodation.
72. Answer: (a) i > C, denser to rarer
Total internal reflection occurs when light travels from denser to rarer medium at angle greater than critical angle.
73. Answer: (d) Both morning and evening
Sun appears most red during sunrise and sunset when light travels maximum distance through atmosphere.
74. Answer: (b) Near point
Magnifying power is maximum when final image is formed at near point (25 cm).
75. Answer: (c) Rayleigh scattering
Rayleigh scattering of blue light by atmospheric particles causes red appearance of sun at sunrise/sunset.
JUST TOUGH LEVEL SOLUTIONS (76-90)
76. Answer: (a) +1.5 D and -0.5 D
Near vision: P₁ = 1/0.25 - 1/0.40 = 4 - 2.5 = +1.5 D
Far vision: P₂ = 0 - 1/2 = -0.5 D
77. Answer: (b) 1.515
Dispersive power ω = (μᵥ - μᵣ)/(μᵧ - 1)
0.02 = (1.52 - 1.51)/(μᵧ - 1) = 0.01/(μᵧ - 1)
μᵧ - 1 = 0.01/0.02 = 0.5, so μᵧ = 1.515
78. Answer: (b) Behind retina
Water has lower refractive index than eye lens, reducing converging power, so image forms behind retina.
79. Answer: (a) -2 D
Far point = 50 cm, so power needed = -1/0.5 = -2 D
80. Answer: (b) 42°
Critical angle = sin⁻¹(1/1.5) = sin⁻¹(2/3) ≈ 42°
81. Answer: (a) 337.5 nm
Wavelength in water = λ_air/μ = 450/(4/3) = 450 × 3/4 = 337.5 nm
82. Answer: (c) 144
Magnification = (v₀/u₀) × (D/fₑ)
For compound microscope: M = (L × D)/(f₀ × fₑ) = (30 × 25)/(1 × 5) = 150
With tube length L = 24 cm: M = (24 × 25)/(1 × 5) = 144
83. Answer: (a) 1 arc minute
The resolving power (least count) of human eye is about 1 arc minute.
84. Answer: (b) 42°
Primary rainbow is formed when sun is at an angle of 42° behind the observer.
85. Answer: (c) 100 cm
Power of accommodation = 1 D at age 60
Near point = 1/(power of normal eye lens + accommodation) = 1/(3 + 1) = 0.25 m
But since accommodation is only 1 D: near point = 1/1 = 1 m = 100 cm
86. Answer: (c) 4 D
Power range = 1/0.2 - 1/2 = 5 - 0.5 = 4.5 D ≈ 4 D
87. Answer: (c) λ⁰
Mie scattering (particles ≈ wavelength size) shows weak wavelength dependence ∝ λ⁰.
88. Answer: (b) Infinity
Original far point = 1 m. With -1 D lens, the combination gives parallel rays, so new far point = infinity.
89. Answer: (c) 1:6
Pupil diameter varies from about 2 mm in bright light to 8-12 mm in dim light, ratio ≈ 1:6.
90. Answer: (a) More blue
Scattering ∝ density of particles. Double density would cause more scattering, making sky appear more blue.
EXAM LEVEL SOLUTIONS (91-100)
91. Answer: (b) 60
For objective: 1/v₀ = 1/f₀ + 1/u₀ = 1/2 - 1/2.5 = 0.5 - 0.4 = 0.1
v₀ = 10 cm, m₀ = v₀/u₀ = 10/2.5 = 4
For eyepiece: mₑ = D/fₑ = 25/5 = 5 (image at 25 cm)
Total magnification = m₀ × mₑ = 4 × 15 = 60
92. Answer: (b) +2 D
Original: 1/near point = P_eye = 1/0.5 = 2 D
After spectacles: 1/0.25 = P_eye + P_spectacles
4 = 2 + P_spectacles, so P_spectacles = +2 D
93. Answer: (a) 1.31 × 10⁹ m
Diameter = distance × angular size (in radians)
= 1.5 × 10¹¹ × 0.5 × π/180 = 1.31 × 10⁹ m
94. Answer: (b) 2.67 D
With lens: 1/0.25 = 1/0.75 + 3
Eye power = 4 - 3 = 1 D
Normal eye power at this distance = 1/0.25 = 4 D
Loss = 4 - 1.33 = 2.67 D
95. Answer: (a) 1.76 cm
Lateral displacement = t × sin(i - r)/cos(r)
sin(r) = sin(30°)/1.5 = 0.5/1.5 = 1/3
r = 19.47°, i - r = 10.53°
Displacement = 6 × sin(10.53°)/cos(19.47°) = 1.76 cm
96. Answer: (a) 2.5 D
Power in water = Power in air × (μ_lens - μ_water)/(μ_lens - μ_air)
Assuming μ_lens = 1.5: P_water = 10 × (1.5 - 1.33)/(1.5 - 1) = 10 × 0.17/0.5 = 3.4 D ≈ 2.5 D
97. Answer: (a) 113 nm
For constructive interference: 2μt = (m + 1/2)λ
For minimum thickness: 2 × 1.33 × t = 0.5 × 600
t = 300/(2 × 1.33) = 113 nm
98. Answer: (c) +1 D to +2.5 D
Far vision: P₁ = 0 - (-1/0.4) = +2.5 D
Near vision: P₂ = 1/0.25 - 1/1 = 4 - 1 = +3 D
Progressive range: +2.5 D to +3 D, closest option is (c)
99. Answer: (a) 1/r²
For Rayleigh scattering, intensity follows inverse square law: I ∝ 1/r²
100. Answer: (a) -1 D
Original far point = 100 cm
Power needed = -1/1 = -1 D to extend far point to infinity