# Compound Lenses - Thin Lenses In Contact

A simple lens system consists of the use of only one lens as opposed to compound lens system where multiple lenses can be used with a single common axis. The simplest of these compound lens systems are two thin lenses kept in contact with each other. Lets study about compound lenses and properties of them.

The common focal length for a system, where two thin lenses are sharing an axis are kept in contact with each other, is given by the following formula.

$\frac{1}{f} = \frac{1}{f1} + \frac{1}{f2}$

where,

f is the combined focal length

f1 is the focal length of the first lens

f2 is the focal length of the second lens

Since the power is the reciprocal of the focal length, what is very evident in this case? For thin lenses in contact, it is pretty clear that the combined power of the system is given by adding the powers of the individual lenses.

But what if the lenses aren’t in contact with each other? If the lenses are separated by a distance‘d’, then in this case the combined focal length can be calculated using the following formula.

$\frac{1}{f} = \frac{1}{f1} + \frac{1}{f2} – \frac{d}{f1.f2}$

Why don’t you try to solve the following simple problem to see if you understand the concept? A bi-convex lens of focal length = 10 cm and a bi-concave lens of focal length = 20 are kept in contact with each other. Both of these have the same value of refractive index. Find the combined focal length.

While dealing with the combination of lenses or compound lenses, you may come across the following terms.

### Afocal System

When the distance of separation between the two lenses (d) if equal to the sum of the individual focal lengths (f1 + f2), the combined focal length is infinite. This makes the refracted light rays parallel to each other.

### Achromatic Doublet

The lenses used are combined in such a way that two wavelengths (typically the ends red and violet), are brought into focus. This is one of the applications of using a compound lens system, where chromatic aberrations (which can be found using single lenses) are corrected.

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#### Practise This Question

A lens of power + 2 diopters is placed in contact with a lens of power – 1 diopter. The combination will behave like