Question
Show that placing a 1-diopter lens in front of a 2-diopter lens gives the equivalent of a single 3 -diopter lens (i.e., the powers of closely spaced lenses add).
Step 1
First, let's understand what diopters represent. Diopters are a unit of measurement for the optical power of a lens. The optical power of a lens is the degree to which it converges or diverges light. A positive diopter value indicates a converging (convex) lens, Show more…
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Show that placing a 1 -diopter lens in front of a 2 -diopter lens gives the equivalent of a single 3 -diopter lens (i.e., the powers of closely spaced lenses add).
Consider a thin positive lens $L_{1},$ and using a ray diagram, show that if a second lens $L_{2}$ is placed at the focal point of $L_{1}$, the magnification does not change. That's a good reason to wear eyeglasses, whose lenses are different, at the correct distance from the eye.
Show that if two thin lenses are close together $(s,$ the distance between the lenses, is negligibly small), the two lenses can be replaced by a single equivalent lens with focal length $f_{\mathrm{eq}^{-}}$. Find the value of $f_{\mathrm{eq}}$ in terms of $f_{1}$ and $f_{2}.$
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