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Formula Sheet
Explore the fascinating workings of the human eye and the science behind the colorful world we perceive, including vision defects and the dispersion of light.
The Human Eye and the Colourful World – Formula & Equation Sheet
Essential formulas and equations from Science, tailored for Class X in Science.
This one-pager compiles key formulas and equations from the 'The Human Eye and the Colourful World' chapter of Science. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
Power of Accommodation
The ability of the eye lens to adjust its focal length to see objects at varying distances clearly. It decreases with age, leading to presbyopia.
Least Distance of Distinct Vision (D) = 25 cm
The minimum distance at which the eye can see objects clearly without strain. For a normal young adult, D is about 25 cm.
Far Point of Normal Eye = ∞
The farthest point up to which the eye can see objects clearly. For a normal eye, it is at infinity.
Lens Power (P) = 1/f (in meters)
P is the power of the lens in diopters (D), and f is the focal length in meters. Used to correct vision defects like myopia and hypermetropia.
Myopia Correction: Concave Lens
A concave lens of suitable power is used to diverge light rays before they enter the eye, correcting the image formation for distant objects.
Hypermetropia Correction: Convex Lens
A convex lens converges light rays before they enter the eye, aiding in the correct image formation for nearby objects.
Angle of Deviation (D) in Prism
The angle between the incident ray and the emergent ray after passing through a prism. It depends on the angle of incidence and the prism's material.
Dispersion of Light
The splitting of white light into its constituent colors (VIBGYOR) when passed through a prism, due to different angles of refraction for different colors.
Scattering of Light ∝ 1/λ⁴
Smaller wavelengths (like blue) scatter more than larger wavelengths (like red), explaining the blue color of the sky and the red color at sunrise/sunset.
Tyndall Effect
Scattering of light by colloidal particles making the path of light visible. Explains the visibility of light in fog or smoke-filled rooms.
Equations
Near Point (N) = 1/P + D
For hypermetropia correction, where P is the power of the lens in diopters, and D is the least distance of distinct vision (25 cm).
Far Point (F) = 1/P
For myopia correction, where P is the power of the concave lens in diopters, making the far point seem at infinity.
Prism Formula: μ = sin[(A+D)/2]/sin(A/2)
μ is the refractive index of the prism material, A is the angle of the prism, and D is the angle of minimum deviation.
Refractive Index (μ) = c/v
c is the speed of light in vacuum, and v is the speed of light in the medium. Determines how much light bends when entering a medium.
Snell's Law: μ₁sinθ₁ = μ₂sinθ₂
Relates the angles of incidence (θ₁) and refraction (θ₂) to the refractive indices (μ₁, μ₂) of two media. Fundamental for understanding light bending.
Lens Maker's Formula: 1/f = (μ-1)(1/R₁ - 1/R₂)
f is the focal length, μ is the refractive index of the lens material, and R₁, R₂ are the radii of curvature of the lens surfaces.
Power of Combination of Lenses: P = P₁ + P₂
The total power of two lenses placed in contact is the sum of their individual powers. Useful for designing corrective lenses.
Critical Angle (θc) = sin⁻¹(1/μ)
The angle of incidence beyond which light undergoes total internal reflection. Important for optical fibers and mirages.
Rainbow Angle: θ = 42° for primary rainbow
The angle at which light is dispersed and internally reflected inside raindrops to form a rainbow. Secondary rainbow occurs at 51°.
Scattering Intensity (I) ∝ 1/λ⁴
Rayleigh's scattering law explains why the sky is blue (more scattering of blue light) and sun appears red at sunrise/sunset (less scattering of red light).
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