The trick is that in most cases you can estimate the prescription fairly decently by looking into the eye with an adjustable lens and illumination. Your eye sees things sharp when the optical system in it can focus light onto your retina accurately. However, it is two-way: your retina can only be *seen* sharply from the front if the focus is good. You can [shine a light into the patient’s eye through lenses and observe the reflection from inside the eyeball](https://www.youtube.com/watch?v=kAreDffuVCQ) to check if the lens you are trying causes the retina to be illuminated just right. The [autorefractor](https://en.wikipedia.org/wiki/Autorefractor) is a more modern machine that performs this measurement automatically and more accurately than using the manual method – it basically pans through focus settings while you try to look at an image shown to you until it finds a correction that lets its internal camera see certain stuff inside your eye in sharp contrast. This is the machine /u/Michelledelhuman is talking about.
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