Which of the following best defines a lens maker's formula?

The lens maker's formula is fundamentally important in optics as it establishes a relationship between the focal length of a lens, the curvature of its surfaces, and the refractive index of the lens material. This formula helps in designing and assessing lenses used in various optical applications, such as eyeglasses, cameras, and telescopes.

Specifically, the formula can be expressed as follows:

[

\frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)

]

Here, ( f ) represents the focal length, ( n ) is the refractive index of the lens material, and ( R_1 ) and ( R_2 ) are the radii of curvature of the lens surfaces. By understanding this relationship, one can manipulate the curvature and lens material to achieve the desired optical properties. The correct answer accurately encapsulates this key relationship that is crucial for designing optical systems effectively.