A spherometer is used to measure

The correct answer is Radius of curvature of a lens.

Step-by-Step Explanation:

1. Understanding the Instrument:
A spherometer is a precision instrument whose name is derived from "sphere" and "meter". As the name suggests, it is designed to measure the properties of spherical surfaces.

2. Working Principle:
The spherometer consists of a central screw that can be raised or lowered relative to a triangular base with three fixed legs. By measuring the small height difference (known as the sagitta, h) between the apex of the spherical surface and the plane passing through the three outer legs, the radius of curvature of the spherical surface can be calculated.

3. The Formula:
Using the measurements from a spherometer, the radius of curvature ($R$) of a spherical surface (like a lens or a curved mirror) is calculated using the formula:
$R=\frac{l^2}{6h}+\frac{h}{2}$
where $l$ is the average distance between any two legs of the spherometer and $h$ is the height of the curved surface above or below the flat plane.

4. Analyzing the Options:
- Radius of curvature of a lens: This fits the exact purpose of a spherometer, as lenses have spherical surfaces.
- Length of rod: A vernier caliper, slide caliper, or screw gauge is typically used to measure the length of a rod.
- Density of a solid: Measured using a balance (for mass) and a graduated cylinder or Archimedes' principle method (for volume).
- Viscosity of a liquid: Measured using a viscometer (such as Ostwald's viscometer or falling sphere methods).

Therefore, a spherometer is specifically used to measure the radius of curvature of a lens.