The Human Eye and the Colourful World — Karnataka (SSLC) Class 10 Science Solutions (Free)

Key structures of the eye and their roles: - Cornea: the transparent outer layer that performs most of the eye's total light bending (refraction), gathering incoming light toward the lens. - Lens: a flexible, transparent structure that fine-tunes the focus, adjusting its own shape to bring light from objects at different distances into sharp focus on the retina. - Retina: the light-sensitive layer at the back of the eye, containing photoreceptor cells that convert incoming light into electrical signals — this is where the actual image is effectively "formed" and detected. - Optic nerve: carries the electrical signals generated at the retina to the brain, where they are interpreted as vision. Accommodation: the eye's ability to change the FOCAL LENGTH of its own lens, adjusting focus for objects at varying distances. This is achieved by the ciliary muscles surrounding the lens — when they contract, the lens becomes thicker and more curved (shorter focal length, needed for close objects); when they relax, the lens flattens (longer focal length, needed for distant objects). This constant, automatic adjustment is why a healthy eye can shift focus between a nearby book and a distant view almost instantly.

Myopia is a vision defect in which a person can see nearby objects clearly, but distant objects appear blurred. Cause: the eyeball is too long from front to back, or the cornea is excessively curved — either way, incoming light from a distant object is bent too strongly and converges to a focus point IN FRONT OF the retina, rather than exactly on it, producing a blurred image. Correction: a concave (diverging) lens, with negative power, is placed in front of the eye. This lens spreads out (diverges) the incoming parallel rays from a distant object slightly BEFORE they enter the eye, so that the eye's own (overly strong) focusing power now brings them to a focus exactly on the retina instead of in front of it.

Hypermetropia is a vision defect in which a person can see distant objects clearly, but nearby objects appear blurred. Cause: the eyeball is too short from front to back, or the cornea is too flat — light from a nearby object is not bent strongly enough by the eye's own optics, so it would converge to a focus point BEHIND the retina if the retina weren't in the way, producing a blurred image at the retina itself. Correction: a convex (converging) lens, with positive power, is placed in front of the eye. This lens pre-converges the incoming light slightly before it enters the eye, adding to the eye's own focusing power so the combined effect brings the image forward, exactly onto the retina, for near objects.

Dispersion is the separation of white light into its constituent colours (violet, indigo, blue, green, yellow, orange, red — remembered as VIBGYOR) when it passes through a refracting medium like a glass prism. Why a prism causes this: white light is actually a mixture of all these colours, each with a different wavelength. A medium's refractive index is not perfectly constant — it varies slightly depending on the wavelength of light passing through it, being HIGHER for shorter wavelengths (violet) and LOWER for longer wavelengths (red). Since a larger refractive index means light bends more sharply, violet light is refracted (bent) the MOST as it passes through the prism, while red light is refracted the LEAST. This wavelength-dependent difference in bending angle physically separates the originally overlapping colours into a visible spread — the spectrum — with violet deviating furthest from the original path and red deviating least.

Rayleigh scattering describes how light is scattered by particles that are much SMALLER than the light's own wavelength (such as the nitrogen and oxygen molecules that make up most of Earth's atmosphere). A key feature of this scattering is that its intensity is proportional to 1/λ⁴ — meaning shorter wavelengths are scattered dramatically more strongly than longer ones. Blue light (wavelength ≈ 450 nm) is scattered far more intensely than red light (wavelength ≈ 700 nm) by atmospheric molecules. Why the sky is blue during the day: sunlight travelling through the atmosphere has its blue component scattered strongly in all directions by air molecules, so wherever you look in the sky (not directly at the sun), you are seeing scattered blue light arriving from many directions — this is why the sky itself, not just the direction of the sun, appears blue. Why sunsets appear red: at sunrise and sunset, sunlight has to travel through a much LONGER path of atmosphere to reach an observer (since the sun is near the horizon rather than overhead). Over this much longer path, most of the blue light has already been scattered away in other directions before it can reach the observer directly, leaving mainly the longer-wavelength red and orange light to continue straight through and reach the eye — producing the characteristic red-orange colour of a sunset sky.

Presbyopia is an age-related vision defect in which the eye gradually loses its ability to accommodate (change focus) effectively, making it increasingly difficult to focus on nearby objects. Cause: with age, the eye's lens progressively loses its natural elasticity, and the ciliary muscles controlling it also weaken — both reduce how much the lens can change shape, directly reducing the range of accommodation. Typical onset: presbyopia usually becomes noticeable after age 45–50, and is a near-universal, natural part of ageing rather than a disease. Correction: bifocal or progressive lenses are commonly prescribed — a bifocal lens has TWO distinct optical zones in one physical lens: the lower part is convex, correcting for near vision (reading), while the upper part is either left uncorrected or fitted for distance vision, matching whatever the wearer's separate distance vision needs are. This lets one pair of glasses serve both near and far vision without needing to switch between two separate pairs.

The person's far point — the maximum distance at which they can see an object clearly WITHOUT correction — is 2 m. A normal eye's far point is infinity, so the corrective lens must let this person see objects at infinity by making them APPEAR to be at their own far point instead. Step 1: Set up the lens formula for the corrective lens Object: at infinity (a distant object, so 1/u = 0) Required image: at the person's own far point, 2 m in front of the eye, as a VIRTUAL image (same side as the object) — so v = −2 m Step 2: Apply the lens formula, 1/f = 1/v − 1/u 1/f = 1/(−2) − 0 = −1/2 f = −2 m Step 3: Find the power P = 1/f = 1/(−2) = −0.5 D The required lens has a power of −0.5 D (a concave/diverging lens). (The 20 cm reading distance given in the question describes the person's NEAR point — since a normal near point is about 25 cm, a 20 cm near point is actually slightly closer than normal, confirming this person's near vision needs no correction at all; only their distance vision, corrected by the −0.5 D lens above, is affected.)