What should be used to periodically dust the exposed surface of an eyepiece?

Using a camel-hair brush to periodically dust the exposed surface of an eyepiece is the most appropriate choice because camel-hair brushes are soft, flexible, and gentle on sensitive optical surfaces. They effectively remove dust and debris without scratching or damaging the eyepiece coating. This care is vital for maintaining the optics' performance and clarity.

In contrast, paper towels can be abrasive and may leave behind lint or scratches on the surface. Cotton swabs might not cover enough area effectively and could also risk damaging delicate coatings. Compressed air might blow dust into other parts of the instrument instead of removing it, and it could also impart moisture or cause other unintended consequences. Thus, the camel-hair brush stands out as the best tool for this maintenance task.