Derive lens maker formula for convex lens
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in case of convex lens focal length is positive.
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Assumptions;
The following assumptions are taken for the derivation of lens maker formula.
- Let us consider the thin lens shown in the image above with 2 refracting surfaces having the radii of curvatures R1 and R2, respectively.
- Let the refractive indices of the surrounding medium and the lens material be n1 and n2, respectively.
Derivation;
The complete derivation of lens maker formula is described below. Using the formula for refraction at a single spherical surface we can say that
For the first surface,
For the second surface,
Now adding equation (1) and (2),
When u = ∞ and v = f
But Also,
Therefore, we can say that,
Where μ is the refractive index of the material.
Where μ is the refractive index of the material.This is the lens maker formula derivation. Check the limitations of the lens maker’s formula to understand the lens maker formula derivation is a better way.
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