Final answer:
Atropine is the medication that provides the strongest cycloplegia for cycloplegic refraction in children, which is crucial for accurate squint assessment.
Step-by-step explanation:
When performing a cycloplegic refraction for squint assessment in children, the medication that provides the strongest cycloplegia is generally considered to be atropine. Cycloplegic refraction is an important part of assessing refractive errors in the presence of squint, as the agent used temporarily paralyzes the ciliary muscle, thus preventing the eye from changing focus during the examination. Different medications like tropicamide, cyclopentolate, and atropine can be used, but atropine produces the most potent and long-lasting cycloplegia, making it highly effective for this purpose. However, it is also associated with prolonged action and side effects which must be carefully considered by the eye care professional.