Important Definitions and Equations: The Human Eye and the Colourful World | Science Class 10 PDF Download

Definitions

• Cornea: The transparent front surface of the eye that refracts (bends) light as it enters the eye.
• Iris: The colored part of the eye that controls the size of the pupil, regulating the amount of light entering the eye.
• Pupil: The small, dark opening in the center of the iris that allows light to enter the eye.
• Crystalline lens: Behind the pupil, there is a transparent structure called a lens. By the action of ciliary muscles, it changes its shape to focus light on the retina. It becomes thinner to focus on distant objects and becomes thicker to focus on the nearby objects. 
• Focal length: The distance between the optical center of a lens and its focal point.
• Retina: The innermost layer of the eye that contains light-sensitive cells (rods and cones) and is responsible for forming an image.
• Cones: Cones are the nerve cells that are more sensitive to bright light. They help in detailed central and colour vision.
• Rods: Rods are the optic nerve cells that are more sensitive to dim lights. They help in peripheral vision.
• Optic nerve: The optic nerve is a bundle of nerve fibers that carries visual information from the retina to the brain
• Blind spot: At the junction of the optic nerve and retina, there are no sensory nerve cells. So no vision is possible at that point and is known as a blind spot. 
• Ciliary Muscles: Muscles that change the shape of the eye's lens to focus on objects at different distances (accommodation).
• Power of accomodation: It is the ability of the eye lens to focus near and far objects clearly on the retina by adjusting its focal length.
• Dispersion: The separation of white light into its constituent colors, producing a spectrum.
• Scattering of light: Scattering of light is a phenomenon that occurs when light rays deviate from their straight path after hitting particles in the atmosphere. 
• Tyndall Effect: The Tyndall effect is a phenomenon that occurs when light is scattered by particles in a colloid, making the path of the light visible.

Myopia or Short-Sightedness

Myopia, also known as near-sightedness, is an eye defect that makes it hard to see objects that are far away: 

Cause: Light rays bend incorrectly and focus in front of the retina, instead of on it. This can be due to the shape of the eye or an elongated eyeball. 

Correction: Myopia can be corrected with concave lenses in glasses or contact lenses.

Hypermetropia or Long-Sightedness

 Hypermetropia, also known as far-sightedness or long-sightedness, is an eye defect that makes it difficult to see nearby objects clearly. It occurs when light rays from a nearby object are focused behind the retina instead of on it, making it difficult to form a distinct image. Causes: Eyeball grows too short from front to back, or when there are problems with the shape of your cornea.

Correction:  Convex lenses provide additional focusing power to shift the image from beyond the retina to the retina. 

Presbyopia or Old Sight

 Presbyopia is the gradual loss of your eyes' ability to focus on nearby objects. It's a natural, often annoying part of aging. Presbyopia usually becomes noticeable in your early to mid-40s and continues to worsen until around age 65. 

Atmospheric Refraction

Atmospheric refraction is the bending of light as it passes through the Earth's atmosphere. This happens because the atmosphere is made up of layers with different optical densities.

• Twinkling of stars: They are point source of light and atmospheric refraction causes bending of light. Apparent image is higher than actual image and causes twinkling effect. 
• Planets do not twinkle, as they are not point source of light
• Early sunrise and late sunset: Sun can be seen two minutes before actual sunrise and two minutes after sunset due to atmospheric refraction.

Formulae

• Lens Formula: 
  where f is the focal length, v is the image distance, and u is the object distance.

• Magnification (m): 
  (Negative sign indicates the inversion of the image formed by the lens)

Power of Accommodation

• Least Distance of Distinct Vision (D):
  • The minimum distance at which the eye can see objects distinctly without strain.

Defects of Vision and Their Correction

(a) Myopia

• Lens Power for Myopia (concave lens): 
  

(b) Hypermetropia

• Lens Power for Hypermetropia (convex lens):
  

(c) Presbyopia

• The loss of accommodation with age.

Refraction of Light Through a Prism

• Angle of Deviation (Δ):
  • The angle through which a ray of light is deviated by a prism.

Dispersion of White Light by a Glass Prism

• Refractive Index (n): 
  where A is the angle of the prism, and δ is the angle of minimum deviation.

Atmospheric Refraction

• Apparent Shift in Position:
  • The apparent position of celestial objects due to atmospheric refraction.

Scattering of Light

(a) Tyndall Effect

• The scattering of light by colloidal particles.

(b) Why is the Colour of the Clear Sky Blue?

• The scattering of shorter wavelengths (blue light) by air molecules in the atmosphere.

These formulas and concepts summarize the key elements of the chapter.