A lens has an index of refraction of 1.7 and a focal length of 12 cm . The front convex surface

step 1 Hi, in the given problem we have been given the refractive index, the index of refraction of the

A lens has an index of refraction of 1.7 and a focal length...

A lens has an index of refraction of 1.7 and a focal length of $12 \mathrm{~cm} .$ The front convex surface of a lens has a radius of curvature of $15 \mathrm{~cm} .$ Calculate the radius of curvature of the back convex surface of the lens.

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Key Concepts

Optical Sign Conventions

Optical sign conventions are guidelines used to assign positive or negative signs to distances, radii of curvature, and focal lengths. These conventions ensure consistency in applying formulas like the lens maker’s equation in optics.

Lens Maker's Formula

This formula relates the focal length of a lens to its radii of curvature and its index of refraction. It is fundamental in optics for understanding how the shape and material of a lens determine its ability to converge or diverge light.

Index of Refraction

The index of refraction is a measure of how much a material slows down light compared to a vacuum. It plays a crucial role in determining how much light is bent, or refracted, when it enters or exits a lens.

Focal Length

The focal length is the distance from the lens where parallel rays of light either converge or appear to diverge after passing through the lens. It is a key parameter in designing optical systems and affects image formation and magnification.

Radius of Curvature

This is the radius of the spherical surface from which a lens surface is derived. It directly influences the degree of light bending at the lens surface and, consequently, the lens's focusing power.

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