Afferent objects at different distances are seen by le eye. The parameter that remains constant is

1. Basics of Light: Refraction and Spherical Lenses (basic)

To understand how we see the world, we must first master the refraction of light through spherical lenses. A lens is a piece of transparent material bound by two surfaces, where at least one surface is spherical. Depending on their shape, lenses behave in two distinct ways: Convex lenses (converging) are thicker at the center and bend light rays inward toward a point, while Concave lenses (diverging) are thinner at the center and spread light rays outward Science, Class X (NCERT 2025 ed.), Chapter 9, p.150. Unlike mirrors that reflect light, lenses allow light to pass through, bending it to form images that can be real (can be caught on a screen) or virtual Science, Class X (NCERT 2025 ed.), Chapter 9, p.158. Every lens has a principal focus and an optical center (O). A key rule in optics is that any ray of light passing through the optical center of a thin lens does so without any deviation Science, Class X (NCERT 2025 ed.), Chapter 9, p.151. To calculate exactly where an image will form, we use the Lens Formula, which defines the relationship between the distance of the object (u), the distance of the image (v), and the focal length of the lens (f):
1/f = 1/v - 1/u
Science, Class X (NCERT 2025 ed.), Chapter 9, p.155. This formula is universal, applying to both convex and concave lenses, provided we follow the Cartesian Sign Convention (where distances in the direction of incident light are positive). In most optical instruments, like a camera, we move the lens back and forth to focus on objects at different distances. However, nature has a more elegant solution. In the human eye, the distance between the lens and the retina (the image distance, v) is fixed at about 2.3 cm. To keep the image sharp on the retina as an object moves (changing u), the eye must change the focal length (f) of its own biological lens Science, Class X (NCERT 2025 ed.), Chapter 10, p.161-162.

Feature	Convex Lens	Concave Lens
Shape	Thicker at the middle	Thinner at the middle
Action on Light	Converging (bends rays inward)	Diverging (bends rays outward)
Image Type	Real or Virtual (depends on position)	Always Virtual (for real objects)

Sources: Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.150, 151, 155, 158; Science, Class X (NCERT 2025 ed.), Chapter 10: The Human Eye and the Colourful World, p.161, 162; Science, Class VIII, NCERT (Revised ed 2025), Chapter 10: Light: Mirrors and Lenses, p.163

2. Anatomy of the Human Eye as an Optical Instrument (basic)

To understand the human eye as an optical instrument, think of it as a biological camera. The eyeball is a nearly spherical structure with a diameter of approximately 2.3 cm Science, Class X (NCERT 2025 ed.), Chapter 10, p. 161. Light enters through a transparent membrane called the cornea, which actually performs the bulk of the light refraction. Behind it, the iris (a muscular diaphragm) adjusts the size of the pupil to control how much light enters, much like an aperture in a camera. The light then passes through the crystalline lens, which forms a real and inverted image on the retina — the light-sensitive 'screen' at the back of the eye Science, Class X (NCERT 2025 ed.), Chapter 10, p. 162.

From the perspective of geometrical optics, the eye operates under a unique constraint. In the lens formula (1/f = 1/v - 1/u), the image distance (v) in the eye is fixed because the distance between the lens and the retina cannot change. When the object distance (u) varies — for instance, when you look from a distant mountain to a book in your hand — the eye must adjust its focal length (f) to ensure the image still lands perfectly on the retina. This is achieved by the ciliary muscles, which modify the curvature of the flexible, jelly-like lens.

This physiological adjustment is known as accommodation. When you look at distant objects, the ciliary muscles relax, making the lens thinner and increasing its focal length. Conversely, when looking at nearby objects, the muscles contract, making the lens thicker (more curved) and decreasing its focal length Science, Class X (NCERT 2025 ed.), Chapter 10, p. 162.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 10: The Human Eye and the Colourful World, p.161; Science, Class X (NCERT 2025 ed.), Chapter 10: The Human Eye and the Colourful World, p.162

3. The Lens Formula and Sign Convention (intermediate)

To master optics, we must first master the New Cartesian Sign Convention. Think of the lens as being placed on a standard coordinate graph where the optical center of the lens is the origin (0,0). Just like in math, distances measured to the right of the origin are positive (+), while those to the left are negative (-). Since we conventionally place the object to the left of the lens, the object distance (u) is almost always taken as negative Science, Class X (NCERT 2025 ed.), Chapter 9, p.142. For the vertical axis, heights measured upward from the principal axis are positive, and downward are negative.

Once we have our signs straight, we apply the Lens Formula: 1/v - 1/u = 1/f. This elegant equation links the object distance (u), the image distance (v), and the focal length (f). It is vital to remember that the focal length of a convex lens is always considered positive, whereas the focal length of a concave lens is negative Science, Class X (NCERT 2025 ed.), Chapter 9, p.155. This formula is universal; it works for both real and virtual images across all spherical lenses, provided you plug in the values with their correct signs.

An fascinating application of this formula is found right inside your head! The human eye acts like a camera where the retina is a fixed screen. Because the distance between your eye's lens and the retina (the image distance, v) is fixed at about 2.3 cm, your eye cannot move the retina back and forth to focus. Instead, it uses ciliary muscles to change the curvature of the lens, thereby adjusting the focal length (f) to match the changing object distance (u). This physiological magic is called accommodation Science, Class X (NCERT 2025 ed.), Chapter 10, p.161-162.

Finally, we define the Power of a lens (P) as the reciprocal of its focal length in meters (P = 1/f). Measured in Dioptres (D), a positive power indicates a converging (convex) lens, while a negative power indicates a diverging (concave) lens Science, Class X (NCERT 2025 ed.), Chapter 9, p.158.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.142, 155, 158; Science, Class X (NCERT 2025 ed.), Chapter 10: The Human Eye and the Colourful World, p.161-162

4. Common Defects of Vision and Their Corrections (intermediate)

To understand vision defects, we must first appreciate the healthy eye's remarkable Power of Accommodation. The eye functions like a camera where the distance between the lens and the retina (the screen) is fixed—roughly 2.3 cm to 2.5 cm. To see objects at different distances clearly, the ciliary muscles must change the curvature of the crystalline lens, thereby adjusting its focal length (f) so the image always lands precisely on the retina Science, Class X (NCERT 2025 ed.), Chapter 10, p.162. When this delicate balance fails due to changes in eyeball shape or muscle flexibility, we experience refractive defects.

The two most common defects are Myopia and Hypermetropia. In Myopia (near-sightedness), a person can see nearby objects clearly but distant objects appear blurred because the image forms in front of the retina. This happens if the eyeball is too long or the lens curvature is too high. Conversely, in Hypermetropia (far-sightedness), distant objects are clear but near objects are blurry because the image forms behind the retina, often due to a short eyeball or a lens with too long a focal length Science, Class X (NCERT 2025 ed.), Chapter 10, p.163.

Defect	Common Name	Image Formation	Correction Lens
Myopia	Near-sightedness	In front of retina	Concave (Diverging)
Hypermetropia	Far-sightedness	Behind retina	Convex (Converging)

As we age, we may encounter Presbyopia. This occurs because the ciliary muscles weaken and the eye lens loses its flexibility, making it difficult to focus on nearby objects. Some individuals suffer from both myopia and hypermetropia simultaneously; they typically require bi-focal lenses, where the upper portion is concave for distance and the lower portion is convex for reading Science, Class X (NCERT 2025 ed.), Chapter 10, p.164.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 10: The Human Eye and the Colourful World, p.162-164

5. Atmospheric Refraction and Scattering of Light (intermediate)

In our study of geometrical optics, we often assume light travels in perfectly straight lines. However, when light enters the Earth’s atmosphere, it encounters a medium that is far from uniform. The Atmospheric Refraction of light occurs because the air density—and consequently the refractive index—gradually increases as we move from space toward the Earth’s surface. This gradient causes light rays to bend continuously toward the normal as they enter the thicker layers of air near the surface.

This bending has fascinating consequences for how we perceive celestial objects. For instance, stars appear slightly higher in the sky than their actual positions, a phenomenon most pronounced when they are near the horizon. Furthermore, the twinkling of stars is not an inherent property of the star itself, but a result of the Earth’s turbulent atmosphere. Because the physical conditions of the air (temperature and density) are constantly shifting, the refractive index of the path through which starlight travels keeps changing. This causes the apparent position and brightness of the star to fluctuate rapidly, creating the twinkling effect. Science, Class X (NCERT 2025 ed.), Chapter 10, p.168

Phenomenon	Primary Cause	Observed Effect
Early Sunrise/Delayed Sunset	Atmospheric Refraction	The sun appears above the horizon about 2 minutes before it actually crosses it.
Blue Sky	Rayleigh Scattering	Fine gas molecules scatter shorter wavelengths (blue) more effectively than longer ones.
White Clouds	Large-particle Scattering	Large water droplets scatter all wavelengths of light almost equally.

Beyond refraction, we must consider Scattering of Light, which occurs when light hits tiny particles in the atmosphere. The Tyndall Effect is the visible path of light created when it is scattered by colloidal particles like dust or mist. Science, Class X (NCERT 2025 ed.), Chapter 10, p.169 The color we see depends on the size of these particles: very fine particles (like nitrogen or oxygen molecules) scatter shorter wavelengths (blue/violet), while larger particles (like dust or water droplets) scatter longer wavelengths or even all wavelengths, making the light appear white. Physical Geography by PMF IAS, Horizontal Distribution of Temperature, p.283 This explains why the sky is blue during the day but turns reddish during sunset, as the light has to travel through a thicker layer of atmosphere, scattering away the blue light and leaving only the longer red wavelengths to reach our eyes.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 10: The Human Eye and the Colourful World, p.168-169; Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.255; Physical Geography by PMF IAS, Horizontal Distribution of Temperature, p.283

6. Power of Accommodation of the Human Eye (exam-level)

In geometrical optics, the Lens Formula (1/f = 1/v - 1/u) tells us that for a fixed focal length, if the object distance (u) changes, the image distance (v) must also change. However, the human eye is biologically unique. The distance between our eye lens and the retina (the screen) is fixed by the physical size of the eyeball, typically around 2.3 cm to 2.5 cm. Since the image distance (v) cannot change, the eye must instead vary its focal length (f) to ensure that light from objects at different distances always converges exactly on the retina. This remarkable physiological ability is known as the Power of Accommodation Science, Chapter 10, p.162.

This adjustment is managed by the ciliary muscles, which surround the crystalline lens. The lens itself is not a rigid piece of glass but a flexible, jelly-like fibrous material. By contracting or relaxing, these muscles modify the curvature of the lens, thereby changing its optical power. When the eye focuses on distant objects, it enters a state of rest, whereas focusing on nearby objects requires active muscular effort Science, Chapter 10, p.162.

Feature	Distant Vision (Far Point)	Near Vision (Near Point)
Ciliary Muscles	Relaxed	Contracted
Lens Shape	Thin / Flattened	Thick / Rounded
Focal Length	Increases (Maximum)	Decreases (Minimum)
Converging Power	Lower	Higher

There are physical limits to this accommodation. The Far Point for a normal eye is infinity, while the Near Point (or the Least Distance of Distinct Vision) is approximately 25 cm for a young adult Science, Chapter 10, p.163. If an object is placed closer than 25 cm, the ciliary muscles cannot strain enough to shorten the focal length further, resulting in a blurred image. As we age, the lens loses its flexibility and the ciliary muscles weaken, a condition known as Presbyopia, which reduces this power of accommodation Science, Chapter 10, p.163.

Sources: Science (NCERT 2025 ed.), Chapter 10: The Human Eye and the Colourful World, p.162; Science (NCERT 2025 ed.), Chapter 10: The Human Eye and the Colourful World, p.163

7. Solving the Original PYQ (exam-level)

This question brings together your understanding of the lens formula and the biological anatomy of the human eye. In a standard laboratory setup, changing the object distance (u) would typically result in a change in the image distance (v) unless the lens itself adapts. As you have learned from Science, Class X (NCERT), the eye is a unique optical system where the "screen"—the retina—is at a fixed anatomical position. For a clear image to be formed, the light rays must always converge precisely on this retinal plane, regardless of how far away the object is.

To arrive at the correct answer, you must apply the principle of accommodation. Since the distance between the eye lens and the retina is physically fixed by the dimensions of the eyeball, the image distance (v) must remain constant. To compensate for varying object distances, the ciliary muscles modify the radii of curvature of the crystalline lens, which in turn alters the focal length. Therefore, while the lens physically reshapes itself to maintain focus, the destination of the light (the image distance) never shifts. This makes (D) the image distance from the eye lens the only logical constant.

UPSC often includes options like focal length and radii of curvature as traps because these are the parameters that actively change to facilitate vision. If the focal length remained constant (Option A), you would only be able to see objects at one specific distance clearly. Similarly, object distance (Option B) is the independent variable mentioned in the prompt itself ("different distances"). By recognizing that the retina acts as a fixed-position sensor, you can easily avoid these distractors and focus on the spatial relationship between the lens and the retina.