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Formula Sheet
Explore the principles of light behavior, including reflection and refraction, and understand how these phenomena shape our perception of the world.
Light – Reflection and Refraction – 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 Light – Reflection and Refraction chapter of Science. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
Mirror Formula: 1/v + 1/u = 1/f
v is image distance, u is object distance, and f is focal length of the mirror. This formula relates the positions of the object and image to the mirror's focal length. Used to find image location.
Magnification (m) = h'/h = -v/u
h' is image height, h is object height, v is image distance, u is object distance. Negative sign indicates inversion. Determines size and nature of the image.
Refractive Index (n) = c/v
c is speed of light in vacuum, v is speed of light in medium. Measures how much light bends when entering a medium. Higher n means more bending.
Snell’s Law: n₁ sinθ₁ = n₂ sinθ₂
n₁ and n₂ are refractive indices of two media, θ₁ and θ₂ are angles of incidence and refraction. Predicts the bending of light at an interface.
Lens Formula: 1/v - 1/u = 1/f
v is image distance, u is object distance, f is focal length of the lens. Similar to mirror formula but with a sign change. Used for lens image calculations.
Power of a Lens (P) = 1/f
f is focal length in meters. P is measured in diopters (D). Positive for convex lenses, negative for concave. Indicates lens strength.
Focal Length (f) = R/2
R is radius of curvature of a spherical mirror. Relates mirror's curvature to its focusing ability. Only valid for small apertures.
Critical Angle (θc) = sin⁻¹(n₂/n₁)
n₁ is refractive index of denser medium, n₂ is rarer medium. Angle beyond which total internal reflection occurs. Important for optical fibers.
Total Magnification for Two Lenses: m = m₁ × m₂
m₁ and m₂ are magnifications of individual lenses. Used when two lenses are combined. Multiplicative property of magnification.
Combined Power of Lenses: P = P₁ + P₂
P₁ and P₂ are powers of individual lenses. Algebraic sum gives total power. Useful for correcting vision with multiple lenses.
Equations
Laws of Reflection: i = r
i is angle of incidence, r is angle of reflection. Both angles are measured from the normal. Fundamental to all mirror problems.
Real Image Formation by Concave Mirror: u > f
u is object distance, f is focal length. Condition for real image formation. Real images are inverted and can be projected.
Virtual Image Formation by Convex Mirror: Always
Convex mirrors always produce virtual, erect, and diminished images. Used in rear-view mirrors for wider field of view.
Lens Maker’s Formula: 1/f = (n-1)(1/R₁ - 1/R₂)
n is refractive index of lens material, R₁ and R₂ are radii of curvature of lens surfaces. Derives focal length from lens geometry.
Linear Magnification for Lenses: m = v/u
v is image distance, u is object distance. Positive m indicates erect image, negative for inverted. Relates image size to object size.
Dispersion Formula: n = A + B/λ²
A and B are material constants, λ is wavelength. Explains separation of light into colors by prism due to wavelength-dependent n.
Power of Combination of Lenses: P_eq = P₁ + P₂ - dP₁P₂
d is distance between lenses. For thin lenses in contact, d=0 simplifies to P_eq = P₁ + P₂. Calculates effective power of lens systems.
Apparent Depth: Real Depth / n
n is refractive index of medium. Explains why objects in water appear shallower. Used in fish-eye view calculations.
Critical Angle Condition: sinθc = n₂/n₁
n₁ > n₂ for total internal reflection. Defines minimum angle for light to be totally reflected back into denser medium.
Focal Length of Concave Lens: Negative
By convention, concave lenses have negative focal lengths. Indicates diverging nature. Important for sign conventions in calculations.
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