Coordinate Geometric Approach to Spherometer

TL;DR

This paper introduces a coordinate geometry method for spherometers that not only confirms the traditional results for spherical surfaces but also extends to aspherical surfaces, offering a new analytical approach.

Contribution

The paper presents a coordinate geometry framework for spherometers, enabling analysis of both spherical and aspherical surfaces, which is a novel extension of traditional geometric methods.

Findings

Reproduces known spherometer results for spheres

Provides a scheme for studying aspherical surfaces

Discusses modifications of spherometers

Abstract

The spherometer used for measuring radius of curvature of spherical surfaces is explicitly based on a geometric relation unique to circles and spheres. We present an alternate approach using coordinate geometry, which reproduces the well-known result for the spherometer and also leads to a scheme to study aspherical surfaces. We shall also briefly describe some of the modified spherometers.