The left face of a biconvex lens has a radius of curvature...

The left face of a biconvex lens has a radius of curvature of magnitude $12.0 \mathrm{cm},$ and the right face has a radius of curvature of magnitude $18.0 \mathrm{cm} .$ The index of refraction of the glass is 1.44 . ( a) Calculate the focal length of the lens. (b) What If? Calculate the focal length the lens has after is turned around to interchange the radii of curvature of the two faces.

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Key Concepts

Lensmaker’s Equation

This fundamental formula relates the focal length of a lens to its index of refraction and the radii of curvature of its two surfaces. It shows how the curvature of the lens surfaces and the material’s refractive properties combine to determine the lens’s ability to converge or diverge light.

Radii of Curvature

These are the distances from the center of curvature to the lens surfaces, indicating how curved each surface is. In lens calculations, both the magnitude and sign (based on the chosen convention) are used, as they critically affect the outcome of the lensmaker’s formula.

Index of Refraction

This is a measure of how much light slows down in a material compared to its speed in a vacuum. It is an essential parameter in optical equations because it influences the bending of light rays as they pass through the lens.

Sign Conventions in Optics

These conventions help determine the proper signs for quantities like radii of curvature, distances, and focal lengths in optical calculations. Using the correct sign conventions ensures that formulas such as the lensmaker’s equation yield accurate and meaningful results.

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