A plano-convex lens of unknown material and unknown focal length is...

A spherometer is a device that does just as the name suggests: it measures a sphere. But what exactly would you measure on a sphere? You could measure its diameter or the circumference of a great circle, the surface area, or the radius. But all of these measurements will change proportionally to the radius $R$ of the sphere. Any surface that is curved has a radius of curvature, the radius of the sphere that approximates the surface locally. Thus, a spherometer can measure the radius of curvature of an item such as a lens and curved mirrors that are spherical.