The fundamental lens equation is given by: $$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$ where $f$ is the focal length, $d_o$ is the object distance, and $d_i$ is the image distance.  Show more…

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For a convex lens, the focal length $f$ is related to the object distance $p$ and the image distance $q$ by the lens equation $$ \frac{1}{f}=\frac{1}{p}+\frac{1}{q} $$ Find the instantaneous rate of change of $q$ with respect to $p$ in the case where $f$ is constant. Explain the significance of the negative sign in your answer. What happens to $q$ as $p$ increases?

For an object placed near a lens, an image forms on the other side of the lens at a distinct position determined by the distance from the lens to the object. The position of the image is found using the thin lens equation: $$ \frac{1}{f}=\frac{1}{d_{o}}+\frac{1}{d_{i}} $$ where $d_{o}$ is the distance from the object to the lens, $d_{i}$ is the distance from the lens to the image, and $f$ is the focal length of the lens. Solve for the object distance $d_{o}$ in terms of the focal length and image distance.

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For an object placed near a lens, an image forms on the other side of the lens at a distinct position determined by the distance from the lens to the object. The position of the image is found using the thin lens equation: $$ \frac{1}{f}=\frac{1}{d_{o}}+\frac{1}{d_{i}} $$ where $d_{o}$ is the distance from the object to the lens, $d_{i}$ is the distance from the lens to the image, and $f$ is the focal length of the lens. Solve for the object distance $d_{o}$ in terms of the focal length and image distance.

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While in principle a simple convex lens will suffice, in practice a compound lens made up of a number of optical lens elements is required to correct (as much ...

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