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The curved surface of most lenses is a small section of a sphere. This is not the ideal shape and the resulting problem is called spherical aberration. After refraction by the lens the rays do not all pass through the same point. This is especially noticeable with the plane/convex lenses used in medium priced optical instruments. The effect is exaggerated in the diagram below.
The effect can be reduced by sharing the refraction approximately equally between the two lens surfaces.
If the object distance for the lens is large (>25m) then the curved face should be towards the object.
If the object distance is small, the lens is used the other way round.
An alternative method of reducing the spherical aberration of a lens is simply to reduce the aperture using a diaphragm (also called an iris or a stop). Although this reduces the spherical aberration it also reduces the brightness of the image.
The refractive index of the material of which a lens is made is different for different wavelengths (colours) of light. Some dispersion of the light occurs, as with a prism. The resulting false colouring of the image is called chromatic aberration.
This effect can be reduced by having a combination of a convex and a concave lens made of glasses having different refractive indices.
The dispersion caused by the convex lens is just cancelled by the dispersion caused by the concave lens.