The focal length (f) of a lens is the distance between the center of the lens and the point at which the reflected light, of a beam of light travelling parallel to the center line, meets the center line (principal axis). The radius of curvature (r) is the radius of the lens that forms a complete sphere.

Relation between Focal Length and Radius of Curvature in Lens

The focal length and radius of curvature are two important parameters of a lens. The focal length is the distance between the lens and the point where the light rays converge after passing through the lens. The radius of curvature is the radius of the spherical surface of the lens.

Concave Lens

In a concave lens, the radius of curvature is negative. The focal length of a concave lens is given by the formula:

f = -R/2

Where f is the focal length and R is the radius of curvature. This means that the focal length of a concave lens is half the absolute value of the radius of curvature.

Convex Lens

In a convex lens, the radius of curvature is positive. The focal length of a convex lens is given by the formula:

f = R/2n-1

Where f is the focal length, R is the radius of curvature, and n is the refractive index of the lens. This means that the focal length of a convex lens is half the radius of curvature multiplied by (n-1).

Conclusion

In conclusion, the relation between focal length and radius of curvature in a lens depends on the type of lens. In a concave lens, the focal length is half the absolute value of the radius of curvature, while in a convex lens, the focal length is half the radius of curvature multiplied by (n-1).