A contact lens is made of plastic with an index of...

A contact lens is made of plastic with an index of refraction of $1.50 .$ The lens has an outer radius of curvature of $+2.00 \mathrm{cm}$ and an inner radius of curvature of $+2.50 \mathrm{cm} .$
= What is the focal length of the lens?

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Key Concepts

Thin Lens Approximation

The thin lens approximation assumes that the lens thickness is negligible compared to its other dimensions, simplifying the calculation of its focal length. This assumption is commonly used in introductory optics to apply the lensmaker’s equation effectively without accounting for complex thickness-dependent effects.

Index of Refraction

The index of refraction of a material quantifies how much light slows down within the medium compared to its speed in a vacuum. It plays a critical role in light refraction at material boundaries and is essential in calculating the optical behavior of lenses.

Focal Length

The focal length of a lens is the distance from the lens to the point where parallel light rays converge or appear to diverge after refraction. It determines the lens's converging or diverging power and is a fundamental property in the study and application of optical systems.

Lensmaker’s Equation

The lensmaker’s equation provides a way to calculate the focal length of a lens based on its refractive index and the radii of curvature of its surfaces. It integrates the material properties with the lens shape, establishing a core relationship in geometrical optics.

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