Optics

The eye and optical instruments

The eye forms a real, reduced, inverted image on the retina; the crystalline lens changes curvature to focus at different distances. Magnifiers, microscopes, and telescopes use lens systems to reveal detail or distant objects.

The eye forms a real, reduced, inverted image on the retina; the crystalline lens changes curvature to focus at different distances. Magnifiers, microscopes, and telescopes use lens systems to reveal detail or distant objects.

Applications and calculation

Quick check

The eye accommodates by changing the curvature of its crystalline lens so a real, inverted image falls on the retina. For distant vision the lens flattens; for near vision the ciliary muscles make it rounder and increase its optical power. In myopia, a distant object focuses in front of the retina, so a diverging corrective lens is used. Hyperopia is commonly corrected with a converging lens to bring the focus onto the retina. A magnifier is a converging lens that gives an enlarged virtual image when the object is inside its focal length. A microscope combines objective and eyepiece lenses to increase angular magnification.Real optical systems can blur or distort images; aperture, lens quality, and alignment all affect sharpness.

A refracting telescope uses a long-focal-length objective to form a real image of a distant object; a short-focal-length eyepiece views that image at a larger angle. For a relaxed eye, angular magnification is approximately $M=f_{objective}/f_{eyepiece}$. This increases apparent angular size, not the object’s physical size. A camera likewise forms a real image on a sensor; focusing moves a lens so the image plane coincides with the sensor.