Lensmaker's Equation Calculator

Calculate:

Lens Refractive Index (n_lens):

Surrounding Medium Refractive Index (n_medium):

Lens Curvature Radius toward Light Source (r_1):

Lens Curvature Radius away from Light Source (r_2):

Focal Length (f):

1. What is the Lensmaker's Equation?

Definition: The Lensmaker's Equation relates the focal length of a lens to its refractive index and the radii of curvature of its surfaces. It can be solved for different variables:

\[ f = \left[ \left( \frac{n_{lens}}{n_{medium}} - 1 \right) \left( \frac{1}{r_1} - \frac{1}{r_2} \right) \right]^{-1} \] \[ n_{lens} = n_{medium} \left[ \left( \frac{1}{r_1} - \frac{1}{r_2} \right) f + 1 \right] \] \[ n_{medium} = n_{lens} \left[ \left( \frac{1}{r_1} - \frac{1}{r_2} \right) f + 1 \right]^{-1} \] \[ r_1 = \left[ \left( \frac{n_{lens}}{n_{medium}} - 1 \right) f + \frac{1}{r_2} \right]^{-1} \] \[ r_2 = \left[ \frac{1}{r_1} - \left( \frac{n_{lens}}{n_{medium}} - 1 \right) f \right]^{-1} \]

Variables:

\( f \): Focal length of the lens (in meters).
\( n_{lens} \): Refractive index of the lens (dimensionless).
\( n_{medium} \): Refractive index of the surrounding medium (dimensionless).
\( r_1 \): Radius of curvature toward the light source (in meters).
\( r_2 \): Radius of curvature away from the light source (in meters).

Explanation: These equations allow you to calculate the focal length, refractive indices, or radii of curvature of a lens based on the known parameters.

2. Importance of the Lensmaker's Equation

Details: The Lensmaker's Equation is essential in optics for designing and analyzing lenses used in cameras, microscopes, telescopes, and eyeglasses.

3. Using the Calculator

Tips: Select the variable to calculate (defaults to Focal Length \( f \), which disables the \( f \) input). Enter the values for the other parameters with their units (meters for focal length and radii). The input field for the calculated variable will be disabled (grayed out). Click "Calculate" to get the result.

Frequently Asked Questions (FAQ)

Q1: What is the Lensmaker's Equation?
A: The Lensmaker's Equation describes the relationship between a lens's focal length, refractive indices, and radii of curvature.

Q2: What is the refractive index?
A: The refractive index (\( n \)) is a dimensionless number that indicates how much light slows down and bends in a medium.

Q3: What are \( r_1 \) and \( r_2 \)?
A: \( r_1 \) is the radius of curvature of the lens surface nearest the light source, and \( r_2 \) is the radius farthest from it (both in meters).

Q4: Can I use different units?
A: Yes, the calculator supports meters (m), centimeters (cm), and millimeters (mm) for focal length and radii.

Q5: How accurate is this calculator?
A: The calculator is accurate based on the Lensmaker's Equation and input values, assuming ideal lens conditions. Real-world factors like aberrations may introduce variations.

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