When sharing binoculars with a friend, you notice that you have to readjust the focus when he has been using it (he wears glasses, but removes them to use the binoculars). Why?

Binoculars work by gathering more light than the human eye would be able to on its own. They use a set of lenses and prisms to focus the light, providing a magnified and clearer view of distant objects. The focus can be adjusted to suit an individual's vision by changing the distance between the lenses and the user's eyes. When your friend wears glasses, he/she probably has either nearsightedness (can't see distant objects clearly) or farsightedness (can't see near objects clearly). When the glasses are removed, the binoculars must be adjusted to compensate for their unaided vision.

If your friend is nearsighted, his/her eyes focus incoming light in front of the retina instead of directly on it. This causes difficulty in seeing distant objects clearly. To correct this, the binoculars' lenses must be adjusted to bring the light rays into focus on the retina, which requires changing the focus to match the specific lens prescription of your friend's glasses.

If your friend is farsighted, his/her eyes focus incoming light behind the retina instead of directly on it. This causes difficulty in seeing nearby objects clearly. When using binoculars, a farsighted person will need to adjust the focus to compensate for this, bringing the light rays into focus on the retina by altering the distance between the lenses and the wearer's eyes.

The human eye has an ability called accommodation, where the lens changes its shape to focus on objects at different distances. However, when someone has a refractive error such as nearsightedness or farsightedness, the eye is unable to accommodate completely, and the person relies on corrective glasses to see clearly. Since your friend removes their glasses while using the binoculars, their eye's accommodation is not sufficient to clearly view objects at different distances through the binoculars. Therefore, the focus must be adjusted to bring the image into view for the individual's specific refractive error.

Vision can vary greatly from person to person, and even between each eye. When sharing binoculars, it's essential for each person to adjust the focus for their unique vision characteristics, ensuring they have the clearest and most detailed view possible. This is the reason why you need to readjust the focus when your friend has been using the binoculars. In conclusion, the need to readjust the focus of the binoculars when sharing them with a friend who wears glasses but removes them to use the binoculars is due to the differences in vision between the two individuals and how binoculars work to accommodate these differences. Your friend's unaided vision requires the focus to be adjusted so they can properly see through the binoculars.