Which instrument measures the power of spectacle lenses?

The lensmeter is the instrument specifically designed to measure the power of spectacle lenses. It accomplishes this by determining the focal length of the lens and providing measurements that indicate the lens's prescription, including sphere, cylinder, and axis. This is crucial for ensuring that lenses provide the correct vision correction for the wearer.

In the context of the other options, while a pupilometer is used to measure the distance between pupils (interpupillary distance), it does not assess the optical power of lenses. A retinoscope is employed to measure refractive error in the eye by observing the reflection of light from the retina, rather than directly measuring the lenses themselves. A sphygmomanometer is entirely unrelated as it measures blood pressure, not optical properties. Understanding the specific function of each instrument highlights why the lensmeter is the appropriate choice for measuring spectacle lens power.