A spherometer is used to measure

The correct option is Radius of curvature of a lens.

Step-by-step Explanation:

1. What is a spherometer?
A spherometer is an instrument designed to measure very small lengths. It is primarily used to determine the curvature of spherical surfaces, such as lenses or curved mirrors.

2. Working Principle:
It consists of a central screw that can be moved vertically up or down with respect to a three-legged triangular base. By measuring the height of the curved surface (called the sagitta) relative to the flat plane formed by the three legs, we can determine the radius of curvature using the formula:
$R=\frac{l^2}{6h}+\frac{h}{2}$
where $R$ is the radius of curvature, $l$ is the distance between the legs of the spherometer, and $h$ is the height or depth (sagitta).

3. Analyzing the Options:
- Radius of curvature of a lens: This is the primary function of a spherometer, which measures the curvature of spherical surfaces.
- Length of rod: Typically measured using a vernier caliper, screw gauge, or meter scale.
- Density of a solid: Measured using a balance (for mass) and a graduated cylinder or Archimedes' principle setup (for volume).
- Viscosity of a liquid: Measured using a viscometer (e.g., Ostwald's viscometer).

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