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Lensmaker's Formula:
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The Lensmaker's formula relates the focal length of a lens to its refractive index and the radii of curvature of its surfaces. It's a fundamental equation in geometrical optics used to design lenses.
The calculator uses the Lensmaker's formula:
Where:
Explanation: The formula shows that focal length depends on the lens material's refractive properties and the curvature of its surfaces. A more curved surface (smaller radius) results in a shorter focal length.
Details: Accurate focal length calculation is crucial for designing optical systems like cameras, telescopes, microscopes, and eyeglasses. It determines how light converges or diverges when passing through the lens.
Tips: Enter refractive index (typically 1.4-1.7 for glass), both radii of curvature in meters. Use positive values for convex surfaces and negative for concave surfaces relative to the incoming light.
Q1: What's the sign convention for radii?
A: For a surface that is convex toward the incoming light, R is positive. For concave surfaces, R is negative.
Q2: What if one surface is flat?
A: For a flat surface, use R = infinity (∞), which makes 1/R = 0 in the formula.
Q3: Does this work for thick lenses?
A: This is the thin lens approximation. For thick lenses, additional factors must be considered.
Q4: What are typical refractive index values?
A: Common values: crown glass ~1.52, flint glass ~1.62, plastic ~1.49, polycarbonate ~1.59.
Q5: How does focal length affect image formation?
A: Shorter focal lengths produce more magnification but have smaller fields of view, while longer focal lengths provide less magnification but wider fields of view.