Achromatic Lenses

Condition for achromatism of two lenses placed in contact: A lens can be considered to be made up of a number of prisms of gradually increasing refracting angles placed one over the other. Similarly, to achromatism is prisms two lenses of different materials (crown and flint glass) can be used to form an achromatic combination. In the case of prisms, the two prisms are cemented such that their refracting angles are in opposite directions. With a convex lens, the blue rays of light come to focus at a point nearer the lens and with a concave lens and a converging incident beam of light the red rays of light meet the axis at a point nearer the lens. Hence to have an achromatic combination of two lenses, one of the lens should be convex (crown) and the other concave (flint).

C is the convex lens of crown glass and F is the concave lens of flint glass.

Let and be the refracting indices for blue, light of rays of the two materials, ƒ_b, ƒ, ƒ_r and ƒ’_b, ƒ’, ƒ’_r are the corresponding focal lengths of the two lenses and ω and ω’ are the dispersive powers for crown and flint glass respectively.

From (i) and (ii)



Substituting these values in equations (ii), (iii), (v) and (vi)

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