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LENSES 111
and instead of obtaining just one small distinct spot of light, it can readily be seen that a small blurred image will result when the screen is held anywhere between F1 and F2.
This phenomenon is known as Spherical Aberration, and it need scarcely be added that unless this is overcome, sharp and clearly defined images must not be expected. Of course, if the aperture of the lens is reduced by means of stops, this makes the definition less hazy, but even then, when sharp at the centre, the image will still be somewhat indistinct at the edges, or vice versa.
Lenses, however, can be made so that rays of light which diverge from a point on the axis come to a focus at another point on the axis. Such points, as previously stated, are known as the conjugate foci of the lens, and the lens itself is spoken of as an aplanatic lens.
Lenses can be rendered more or less free from spherical aberration by grinding them so that their faces shall have suitable radii of curvature.
Mathematical investigation shows that such conditions are obtained when the two radii are to one another in the
ratio n ^ 0 where u is the refractive index of the glass
used.
The best results are obtained when the rays receive equal amounts of deviation at each surface of the lens. For this purpose light must enter the surface at an angle equal to that at which it emerges from the other, just as in the case of the prism. For this reason plano-convex lenses are often used, the convex surface being placed towards the incident light.
Spherical aberration may also be got rid of by combining different lenses of suitable curvature, as is done in the rapid rectilinear photographic lenses.
Circle of Least Confusion. Astigmatism. — Now suppose a parallel beam of light strikes a spherical refracting surface