Question
Show that the mirror equation for a curved mirror reduces to the mirror equation for a plane mirror $\left(d_{\mathrm{i}}=-d_{\mathrm{o}}\right)$ when the focal length becomes infinite. (This makes sense, because the surface of a sphere with a large radius of curvature appears almost flat, like a plane mirror.)
Step 1
Step 1: The mirror equation for a curved mirror is given by $\frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f}$, where $d_o$ is the object distance, $d_i$ is the image distance, and $f$ is the focal length. Show more…
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Key Concepts
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Show that as the radius of curvature of a concave mirror increases to infinity, the mirror equation reduces to the relationship between the object position and the image position for a plane mirror.
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Show that if a flat mirror is assumed to have an "infinite" radius of curvature, the mirror equation reduces to $q=-p$
A plane mirror essentially has a radius of curvature of infinity. Using the mirror equation, show that (a) the image of a plane mirror is always virtual, (b) the image is "behind" the mirror the same distance as the object is in front of the mirror, and (c) the image is always upright.
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