A coin is located 20.0 cm to the left of a converging lens...

A coin is located $20.0 \mathrm{~cm}$ to the left of a converging lens $(f=16.0 \mathrm{~cm}) .$ A second, identical lens is placed to the right of the first lens in such a way that the image formed by the combination will have the same size and orientation as the original coin. Find the separation between the lenses.

Key Concepts

Thin Lens Equation

This equation, 1/f = 1/do + 1/di, is fundamental for analyzing image formation by lenses. It relates the object distance (do), the image distance (di), and the focal length (f) of a thin lens. Understanding and applying this equation is crucial when calculating where an image will form, as well as when multiple lenses are used in sequence to generate a desired image configuration.

Magnification

Magnification, defined as m = -di/do for a thin lens, indicates the ratio of the image size to the object size and incorporates the sign convention that indicates image inversion. In problems involving multiple lenses, requiring a final image with the same size and orientation as the object imposes conditions on the individual magnifications (such as having a net magnification of +1), which is critical for determining the proper placement and spacing of the lenses.

Multi?Lens System Analysis

In systems with more than one lens, the image formed by the first lens acts as the object for the second lens. Analyzing such systems requires sequential application of the thin lens equation and the magnification formula while carefully tracking distances and orientations using proper sign conventions. This concept is essential for engineering an optical system so that the overall image meets specific characteristics such as size and orientation.

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