Lens Makers Equation Calculator

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✖The Lens Refractive Index is defined as the refractive index of a lens is the ratio of the speed of light in a vacuum divided by the speed of light in the lens material.ⓘ Lens Refractive Index [μ_l]			+10% -10%
✖The Medium Refractive Index is defined as the refractive index of a medium that is dependent upon the frequency of light passing through, with the highest frequencies having the highest values of n.ⓘ Medium Refractive Index [μ_m]			+10% -10%
✖Radius of Curvature at Section 1 is defined as the radius of curvature in mutually perpendicular planes containing a line normal to surface 1 to describe the curvature at any point on surface 1.ⓘ Radius of Curvature at Section 1 [R₁]			+10% -10%
✖Radius of Curvature at Section 2 is defined as the radius of curvature in mutually perpendicular planes containing a line normal to surface 2 to describe the curvature at any point on surface 2.ⓘ Radius of Curvature at Section 2 [R₂]			+10% -10%

✖Focal Length 1 is the focal length of lens 1.ⓘ Lens Makers Equation [f₁]

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Formula

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Lens Makers Equation

Formula

`"f"_{"1"} = ("μ"_{"l"}/"μ"_{"m"}-1)*(1/"R"_{"1"}-1/"R"_{"2"})`

Example

`"3.170831m"=("10"/"1.3"-1)*(1/"1.67m"-1/"8m")`

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Lens Makers Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Focal Length 1 = (Lens Refractive Index/Medium Refractive Index-1)*(1/Radius of Curvature at Section 1-1/Radius of Curvature at Section 2)
f₁ = (μ_l/μ_m-1)*(1/R₁-1/R₂)
This formula uses 5 Variables

Variables Used

Focal Length 1 - (Measured in Meter) - Focal Length 1 is the focal length of lens 1.
Lens Refractive Index - The Lens Refractive Index is defined as the refractive index of a lens is the ratio of the speed of light in a vacuum divided by the speed of light in the lens material.
Medium Refractive Index - The Medium Refractive Index is defined as the refractive index of a medium that is dependent upon the frequency of light passing through, with the highest frequencies having the highest values of n.
Radius of Curvature at Section 1 - (Measured in Meter) - Radius of Curvature at Section 1 is defined as the radius of curvature in mutually perpendicular planes containing a line normal to surface 1 to describe the curvature at any point on surface 1.
Radius of Curvature at Section 2 - (Measured in Meter) - Radius of Curvature at Section 2 is defined as the radius of curvature in mutually perpendicular planes containing a line normal to surface 2 to describe the curvature at any point on surface 2.

STEP 1: Convert Input(s) to Base Unit

Lens Refractive Index: 10 --> No Conversion Required
Medium Refractive Index: 1.3 --> No Conversion Required
Radius of Curvature at Section 1: 1.67 Meter --> 1.67 Meter No Conversion Required
Radius of Curvature at Section 2: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f₁ = (μ_l/μ_m-1)*(1/R₁-1/R₂) --> (10/1.3-1)*(1/1.67-1/8)

Evaluating ... ...

f₁ = 3.17083141409489

STEP 3: Convert Result to Output's Unit

3.17083141409489 Meter --> No Conversion Required

FINAL ANSWER

3.17083141409489 ≈ 3.170831 Meter <-- Focal Length 1

(Calculation completed in 00.004 seconds)

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Home » Physics » Optics » Focal Length of Lens » Lens Makers Equation

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< 6 Focal Length of Lens Calculators

Lens Makers Equation

Go Focal Length 1 = (Lens Refractive Index/Medium Refractive Index-1)*(1/Radius of Curvature at Section 1-1/Radius of Curvature at Section 2)

Focal Length using Distance Formula

Go Focal Length of Lens = (Focal Length 1+Focal Length 2-Width of Lens)/(Focal Length 1*Focal Length 2)

Focal Length of Concave Lens given Image and Object Distance

Go Focal Length of Concave Lens = (Object Distance*Image Distance)/(Image Distance-Object Distance)

Focal Length of Convex Lens given Object and Image Distance

Go Focal Length of Convex Lens = (Object Distance*Image Distance)/(Object Distance-Image Distance)

Focal Length of Concave Lens given Radius

Go Focal Length of Concave Lens = -Radius/2

Focal Length of Convex Lens given Radius

Go Focal Length of Convex Lens = Radius/2

Lens Makers Equation Formula

Focal Length 1 = (Lens Refractive Index/Medium Refractive Index-1)*(1/Radius of Curvature at Section 1-1/Radius of Curvature at Section 2)
f₁ = (μ_l/μ_m-1)*(1/R₁-1/R₂)

What is lens maker formula why is it so called?

Lens Maker's formula is a formula that relates focal length, radii of curvature, and refractive index of the lens. This is so-called as the formula helps lens manufacturers in finding the radii of curvature of the required lens.

How to Calculate Lens Makers Equation?

Lens Makers Equation calculator uses Focal Length 1 = (Lens Refractive Index/Medium Refractive Index-1)*(1/Radius of Curvature at Section 1-1/Radius of Curvature at Section 2) to calculate the Focal Length 1, The lens makers equation formula is defined as the relation between the focal length of a lens to the refractive index of its material and the radii of curvature of its two surfaces. Focal Length 1 is denoted by f₁ symbol.

How to calculate Lens Makers Equation using this online calculator? To use this online calculator for Lens Makers Equation, enter Lens Refractive Index (μ_l), Medium Refractive Index (μ_m), Radius of Curvature at Section 1 (R₁) & Radius of Curvature at Section 2 (R₂) and hit the calculate button. Here is how the Lens Makers Equation calculation can be explained with given input values -> 3.346154 = (10/1.3-1)*(1/1.67-1/8).

FAQ

What is Lens Makers Equation?

The lens makers equation formula is defined as the relation between the focal length of a lens to the refractive index of its material and the radii of curvature of its two surfaces and is represented as f₁ = (μ_l/μ_m-1)*(1/R₁-1/R₂) or Focal Length 1 = (Lens Refractive Index/Medium Refractive Index-1)*(1/Radius of Curvature at Section 1-1/Radius of Curvature at Section 2). The Lens Refractive Index is defined as the refractive index of a lens is the ratio of the speed of light in a vacuum divided by the speed of light in the lens material, The Medium Refractive Index is defined as the refractive index of a medium that is dependent upon the frequency of light passing through, with the highest frequencies having the highest values of n, Radius of Curvature at Section 1 is defined as the radius of curvature in mutually perpendicular planes containing a line normal to surface 1 to describe the curvature at any point on surface 1 & Radius of Curvature at Section 2 is defined as the radius of curvature in mutually perpendicular planes containing a line normal to surface 2 to describe the curvature at any point on surface 2.

How to calculate Lens Makers Equation?

The lens makers equation formula is defined as the relation between the focal length of a lens to the refractive index of its material and the radii of curvature of its two surfaces is calculated using Focal Length 1 = (Lens Refractive Index/Medium Refractive Index-1)*(1/Radius of Curvature at Section 1-1/Radius of Curvature at Section 2). To calculate Lens Makers Equation, you need Lens Refractive Index (μ_l), Medium Refractive Index (μ_m), Radius of Curvature at Section 1 (R₁) & Radius of Curvature at Section 2 (R₂). With our tool, you need to enter the respective value for Lens Refractive Index, Medium Refractive Index, Radius of Curvature at Section 1 & Radius of Curvature at Section 2 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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