Vision and Correcting Lenses

The cornea provides much of the eye’s refraction; the lens changes curvature during accommodation to focus objects at different distances onto the retina. The retinal image is real and inverted. For a nearer object, more converging power is needed. Draw rays from the object through the optical system meeting on the retina.

Rods are highly sensitive in dim conditions but many feed a common nerve pathway, reducing spatial resolution. Cones provide colour information and high spatial resolution, especially in the densely packed fovea where their signals are more individually represented. The response varies with wavelength and lighting: photopic vision is most sensitive in the green-yellow region, while dark-adapted rod vision peaks at a shorter wavelength.

A myopic eye focuses parallel incoming rays in front of the retina and has a finite far point. A diverging corrective lens makes a distant object appear as a virtual image at that far point. Hypermetropia makes nearby focusing difficult: a converging lens makes an object at the desired near distance appear at the eye’s more distant near point.

Use the real-is-positive thin-lens convention here: a real object has positive u, a real image positive v, a virtual image negative v, and a diverging lens negative f. Power is measured in dioptres when f is in metres. For correcting spectacles close to the eye, neglect the lens–eye separation unless it is supplied.

Astigmatism gives different focusing powers in different meridians of the eye. A cylindrical lens changes power in one orientation and is specified by cylinder power and axis; a spherical term supplies power equally in all meridians. A prescription therefore commonly lists sphere (SPH), cylinder (CYL) and axis in degrees. The axis gives the orientation of the cylinder’s zero-power meridian; the perpendicular meridian receives the cylinder correction.

When sketching correction, show the corrective lens changing the ray convergence before rays enter the eye. A list of lens names alone does not explain why the image returns to the retinal plane.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.