What is lens and lens maker formula?

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This comprehensive guide covers all essential lens formulas required for school and college-level physics. Each formula is presented with clear explanations, applications, and sign conventions to ensure complete understanding.1. Fundamental Lens FormulasFormula NameFormulaVariablesApplicationNotesLens Formula (Gaussian Form)1/f = 1/u + 1/vf = focal lengthu = object distancev = image distanceAll types of lensesClass 10 & 12 PhysicsMost important lens equationAlternative Lens Formula1/f = 1/d₀ + 1/dᵢf = focal lengthd₀ = object distancedᵢ = image distanceSame as aboveAlternative notationNewton's Lens Formulaxx' = f²x = distance from object to front focal pointx' = distance from image to back focal pointf = focal lengthAdvanced applicationsClass 12 PhysicsUsed when measuring from focal points2. Lens Maker's FormulaFormula NameFormulaVariablesApplicationNotesLens Maker's Formula (Basic)1/f = (n-1)(1/R₁ - 1/R₂)f = focal lengthn = refractive index of lens materialR₁ = radius of curvature of first surfaceR₂ = radius of curvature of second surfaceDetermining focal length from physical propertiesFor thin lens in airLens Maker's Formula (Medium)1/f = (n₂/n₁ - 1)(1/R₁ - 1/R₂)n₁ = refractive index of mediumn₂ = refractive index of lens materialLens in different mediaWhen lens is not in airLens Maker's Formula (Thick Lens)1/f = (n-1)[1/R₁ - 1/R₂ + (n-1)t/nR₁R₂]t = thickness of lens at centerThick lensesMore accurate for thick lenses3. Magnification FormulasFormula NameFormulaVariablesApplicationNotesLinear Magnificationm = v/u = h'/hm = magnificationv = image distanceu = object distanceh' = image heighth = object heightSize comparison of image and objectNegative m = inverted imageMagnification (Focal Length)m = f/(f-u) = (f-v)/ff = focal lengthWhen focal length is knownUseful for quick calculationsAngular MagnificationM = α'/αα' = angle subtended by imageα = angle subtended by objectMagnifying glasses, telescopesFor visual instrumentsLongitudinal Magnificationmₗ = m²mₗ = longitudinal magnificationm = linear magnificationDepth magnificationFor 3D objects4. Power of Lens FormulasFormula NameFormulaVariablesApplicationNotesPower of LensP = 1/fP = power (in diopters)f = focal length (in meters)Lens prescription, optical instrumentsUnit: Diopter (D) = m⁻¹Power in Different UnitsP = 100/f_cmf_cm = focal length in cmWhen focal length is in cmCommon in practical problemsCombined Power (Contact)P = P₁ + P₂P₁, P₂ = powers of individual lensesTwo thin lenses in contactPowers are additiveCombined Power (Separated)P = P₁ + P₂ - (d·P₁·P₂)/nd = separation distancen = refractive index of mediumTwo lenses separated by distance dMore complex calculation5. Specific Lens Type FormulasConvex Lens (Converging Lens)ParameterFormula/ValueNotesFocal Lengthf > 0 (positive)Real focusFor Real Imagesv > 0, u < 0Image on opposite sideFor Virtual Imagesv < 0, u < 0Image on same side as objectCritical Conditionu = fImage at infinityConcave Lens (Diverging Lens)ParameterFormula/ValueNotesFocal Lengthf < 0 (negative)Virtual focusImage NatureAlways virtual: v < 0Image always on same sideMagnification`0

Formula Name	Formula	Variables	Application	Notes
Lens Formula (Gaussian Form)	`1/f = 1/u + 1/v`	f = focal length u = object distance v = image distance	All types of lenses Class 10 & 12 Physics	Most important lens equation
Alternative Lens Formula	`1/f = 1/d₀ + 1/dᵢ`	f = focal length d₀ = object distance dᵢ = image distance	Same as above	Alternative notation
Newton's Lens Formula	`xx' = f²`	x = distance from object to front focal point x' = distance from image to back focal point f = focal length	Advanced applications Class 12 Physics	Used when measuring from focal points

Formula Name	Formula	Variables	Application	Notes
Lens Maker's Formula (Basic)	`1/f = (n-1)(1/R₁ - 1/R₂)`	f = focal length n = refractive index of lens material R₁ = radius of curvature of first surface R₂ = radius of curvature of second surface	Determining focal length from physical properties	For thin lens in air
Lens Maker's Formula (Medium)	`1/f = (n₂/n₁ - 1)(1/R₁ - 1/R₂)`	n₁ = refractive index of medium n₂ = refractive index of lens material	Lens in different media	When lens is not in air
Lens Maker's Formula (Thick Lens)	`1/f = (n-1)[1/R₁ - 1/R₂ + (n-1)t/nR₁R₂]`	t = thickness of lens at center	Thick lenses	More accurate for thick lenses

Formula Name	Formula	Variables	Application	Notes
Linear Magnification	`m = v/u = h'/h`	m = magnification v = image distance u = object distance h' = image height h = object height	Size comparison of image and object	Negative m = inverted image
Magnification (Focal Length)	`m = f/(f-u) = (f-v)/f`	f = focal length	When focal length is known	Useful for quick calculations
Angular Magnification	`M = α'/α`	α' = angle subtended by image α = angle subtended by object	Magnifying glasses, telescopes	For visual instruments
Longitudinal Magnification	`mₗ = m²`	mₗ = longitudinal magnification m = linear magnification	Depth magnification	For 3D objects

Formula Name	Formula	Variables	Application	Notes
Power of Lens	`P = 1/f`	P = power (in diopters) f = focal length (in meters)	Lens prescription, optical instruments	Unit: Diopter (D) = m⁻¹
Power in Different Units	`P = 100/f_cm`	f_cm = focal length in cm	When focal length is in cm	Common in practical problems
Combined Power (Contact)	`P = P₁ + P₂`	P₁, P₂ = powers of individual lenses	Two thin lenses in contact	Powers are additive
Combined Power (Separated)	`P = P₁ + P₂ - (d·P₁·P₂)/n`	d = separation distance n = refractive index of medium	Two lenses separated by distance d	More complex calculation

Parameter	Formula/Value	Notes
Focal Length	`f > 0` (positive)	Real focus
For Real Images	`v > 0, u < 0`	Image on opposite side
For Virtual Images	`v < 0, u < 0`	Image on same side as object
Critical Condition	`u = f`	Image at infinity

What is lens and lens maker formula?

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Condition	Formula	Application
Thin Lens	`t << f` where t = thickness	Most classroom problems
Principal Planes	Coincide at lens center	Simplifies ray tracing
Nodal Points	Coincide with principal points	For air-glass interface

Quantity	Positive	Negative
Object Distance (u)	Virtual object (rare)	Real object (common)
Image Distance (v)	Real image	Virtual image
Focal Length (f)	Converging lens	Diverging lens
Height (h)	Above principal axis	Below principal axis
Radius of Curvature (R)	Center on image side	Center on object side

Formula Name	Formula	When to Use
Minimum Distance Formula	`D_min = 4f`	Minimum distance between object and real image
Displacement Method	`f = (D² - d²)/(4D)`	D = object-image distance, d = displacement of lens
Bessel's Method	`f = (D² - d²)/(4D)`	Two positions of lens for same magnification
Focal Length from Magnification	`f = u(m-1)/m = v(m-1)`	When magnification is known