Optical Systems lecture 5

Lecture 5
Achromatic lenses
An achromatic lens or achromat is a lens that is designed to limit the effects of chromatic and spherical aberration. Achromatic lenses are corrected to bring two wavelengths (typically red and blue) into focus on the same plane.
The most common type of achromat is the achromatic doublet, which is composed of two individual lenses made from glasses with different amounts of dispersion. Typically, one element is a negative (concave) element made out of flint glass such as F2, which has relatively high dispersion, and the other is a positive (convex) element made of crown glass such as BK7, which has lower dispersion. The lens elements are mounted next to each other, often cemented together, as shown in figure (1-7), and shaped so that the chromatic aberration of one is counterbalanced by that of the other.

The powers of the two lenses for the yellow center of the visible spectrum, conveniently represented by the Fraunhofer wavelength, ?_D=587.6 nm, are
P_1D=1/f_1D =(n_1D-1)[1/r_11 -1/r_12 ]=(n_1D-1) K_1 ……….. (1-1)
P_2D=1/f_2D =(n_2D-1)[1/r_21 -1/r_22 ]=(n_2D-1) K_2 ……….. (1-2)
where the radii of curvature are designated in Figure (1-8).
The focal length f of a thin-lens doublet satisfies the relation:
1/f=1/f_1 +1/f_2 ………….(1-3)
Here, f_1 and f_2 are the focal lengths of the two lenses in the doublet. Consequently, the power of the doublet is:
P=P_1+P_2 …………. (1-4)