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Thermodynamics

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Circle of Least Confusion

For a point object illuminated by white light and situated on the axis of the lens, coloured images are formed along the axis. The blue image is nearest the lens and the red image is the farthest. In between these two images, if the screen is placed at the position XY, the image of the least chromatic aberration is formed.

The diameter of the circle of least confusion is calculated as follows: Let u be the distance of the object point and v_b and v_r the distances of the blue and red images on the axis of the lens. If ƒ_b and ƒ_r are the focal lengths for the blue and red rays of light, then,

Subtracting (ii) from (i)

But, ƒ_r – ƒ_b = ωƒ

Or, Δ's LQN and APB are similar

Δ's LPN and APB are similar

Adding equations (iv) and (v)

But, PQ = v_r – v_b

AB = d, the diameter of the side of the circle of least confusion

LN = D, the diameter of the lens

and, MQ + MP = v_r + v_b = 2v approximately.

Substituting these values in equation (vi),

But, from equation (iii),

where d is the diameter of the circle of least confusion. If a parallel beam of light is incident on the lens, then

v = ƒ and

In this case, d depends on the diameter of lens aperture and the dispersive power of the material, but is dependent of the focal length of the lens.