Final answer:
A muscarinic receptor inhibitor such as phenylephrine, which is an α₁-adrenergic agonist, would be used to dilate the pupils for a retinal examination. The action of such drugs mimics the effects of norepinephrine on the adrenergic receptors in the iris, leading to mydriasis.
Step-by-step explanation:
The type of drug that would be useful in dilating the pupils for an examination of the retina is a muscarinic receptor inhibitor. Phenylephrine is often used for this purpose because it is an α₁-adrenergic agonist, which means it binds to a specific adrenergic receptor, stimulating a response that leads to mydriasis, the dilation of the pupil. This action mimics the natural effect of norepinephrine in the sympathetic nervous system, which causes pupillary dilation when it binds to adrenergic receptors in the iris smooth muscle.