The "miner's hat" is called a Binocular Indirect Ophthalmoscope (or BIO for short). A lens is held in front of the eye during this procedure; nothing is pressed directly against the eye.
Any given optometrist should be doing both slit lamp fundoscopy and binocular indirect ophthalmoscopy each time you visit them, possibly excluding follow-up visits.
Yes, it is a pain to be dilated and not be able to read for three hours, but on the other hand, these procedures can help identify certain conditions which can eventually cause permanent blindness. Most often, this blindness is preventable. Before going to see the eye doctor, make arrangements -- pick up some cheap +1.50 reading glasses and possibly some sunglasses if you plan to be outside after dilation -- and get your fundus checked regularly.