Two thin lenses of focal lengths f1 and f2 are in contact...

Two thin lenses of focal lengths $f_{1}$ and $f_{2}$ are in contact and share the same central axis. Show that, in image formation, they are equivalent to a single thin lens for which the focal length is $f=f_{1} f_{2} /\left(f_{1}+f_{2}\right)$

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Key Concepts

Thin Lens Approximation

This concept assumes that the lens thickness is negligible compared to the object and image distances, allowing simplifications in the analysis of light propagation through the lens. This approximation enables the use of simple formulas, such as the thin lens equation, to relate object distance, image distance, and focal length.

Focal Length and Optical Power

The focal length is a measure of the distance at which parallel rays of light converge (or appear to diverge from) after passing through a lens. Optical power, defined as the inverse of the focal length, quantifies the ability of a lens to converge or diverge light, and is a central concept when analyzing and combining the effects of multiple lenses.

Lens Combination and Effective Focal Length

When two thin lenses are in contact, their individual optical powers add together, resulting in an effective optical power for the composite system. This allows the lens combination to be treated as a single lens with an effective focal length derived from the reciprocal of the sum of the individual powers, which simplifies the analysis of image formation.

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