Physics Study Guide/Print version - Wikibooks, open books for an open world

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Mirrors and lenses

$\frac {1}{d_i} + \frac {1}{d_o} = \frac {1}{f}$

f is the focal length.
- f is negative in convex mirror and concave lens.
- f is positive in concave mirror and convex lens.
d_i is the distance from the image to the mirror or lens
- For a mirror, it is positive if the image appears in front of the mirror. It is negative if the image appears behind.
- For a lens, it is positive if the image appears on the opposite side of the lens as the light source. It is negative if the image appears on the same side of the lens as the light source.

d_o is the distance from the object to the mirror or the lens (always positive). The only case, when it is negative, is the case, when you don't have a real object, but you do have an imaginary object - a converging set of rays from another optical system.
an easy way to remember the formula is to memorize "if I Do I Die", which stands for 1/f = 1/d_0 + 1/d_i

$M = \frac {h_i}{h_o} =-\frac {d_i}{d_o}$

M is the magnification.
- If it is positive the image is upright
- If it is negative the image is inverted
h_i is the image height.
h_o is the object height.
d_i is the distance from the image to the mirror or lens (also often v)
- For a mirror, it is positive if the image appears in front of the mirror. It is negative if the image appears behind.
- For a lens, it is positive if the image appears on the opposite side of the lens as the light source. It is negative if the image appears on the same side of the lens as the light source.
d_o is the distance from the object to the mirror or lens (also often u)