The achromatic doublet

5.1.3 The achromatic doublet

Combining a biconvex crown glass lens with a plano-concave fl int glass lens, gives what is called an achromatic doublet or achromat – implying that the problem of chromatic aberration is largely eliminated. Such a doublet lens was fi rst patented by John Dolland in 1758 but it is believed that the fi rst achromatic lenses were made by Chester Moore Hall in about 1733.

A similar calculation to that above can show how the combination of lenses used by Dolland can markedly reduce the chromatic aberration. We will assume that the plano-concave fl int lens has zero thickness in the middle as any additional path length through the fl int glass due to its minimum thickness is common to both the central and extreme rays and so will cancel out. (Figure 5.6)

Equating the path lengths of the central and extreme rays gives:

f 2 2 1 1/2 ⫺n 2 ⫺ 1) ⫽ (f )

Squaring both sides gives: f 2 1 1 ⫺n ⫺ 1)] 2 ⫽f 2 2 2

Introduction to Astronomy and Cosmology

Figure 5.6 An achromatic doublet.

Cancelling f 2 , ignoring the term in t 2 and simplifying gives:

f ⫽r 2 /2t(2n 1 ⫺n 2 ⫺ 1) Substituting for r 2 , as above, gives: f ⫽ a/(2n 1 ⫺n 2 ⫺ 1)

The calculation shows that the focal length now depends on (2n c ⫺n f ⫺ 1). We can choose a value of a, 393.6 mm, to give the same focal length for green- yellow light as for the biconvex lens so the results can be directly compared. From Table 5.1 this gives for blue, green-yellow and red, respectively:

One can see that the spread in focal length is reduced so helping to eliminate the chromatic aberration. This was for a generic pair of glasses. If the pair of glasses is chosen with care, particularly if one has a very high refractive index or, even better, a lens made of calcium fl uorite, the correction can be extremely

Observing the Universe

good and the resulting doublet lenses effectively colour free. Such lenses are called apochromats and give superb images. Apochromats may also constructed using a combination of three lenses of differing glass types.

Telescopes using an objective lens, either an achromat or an apochromat, are widely used by amateur astronomers in sizes up to ∼150 mm diameter (above 150 mm the cost rises markedly). A pair of binoculars is made up of two short focal length refractors linked together. These employ prisms to fold their light paths and so reduce their overall length as well as to give an erect image.

Many astronomical telescopes now use a combination of lenses and mirrors and these are called catadioptric telescopes. All three types will be described below after a consideration of some general properties of telescopes and why they are employed.

A telescope is used to do two things: (1) To collect more light so that fainter objects can be seen better than

with the unaided eye. (2) To enable us to see greater detail in a distant object.

We will consider each in turn. However, it is important to fi rst understand a little about the human eye which is, after all, a wonderful optical instrument.