Waves and optics

Thin lens equation - formula in LaTeX

The thin lens equation. For a virtual image y is negative, and for a diverging lens the focal length is negative. The three fractions written with \dfrac share the same height, so the equation looks even inline too.

\dfrac{1}{f} = \dfrac{1}{x} + \dfrac{1}{y}

LaTeX code

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$$
\dfrac{1}{f} = \dfrac{1}{x} + \dfrac{1}{y}
$$

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What the symbols mean

$f$: focal length of the lens (m)
$x$: distance from the object to the lens (m)
$y$: distance from the image to the lens (m)

A waves and optics formula - common in interference, refraction and quantum physics problems.

Worked example

An object 15 cm in front of a converging lens with a 10 cm focal length. The image forms 30 cm behind the lens and is twice as large, since the magnification p = y/x = 2. Distances can stay in centimetres as long as they all use the same unit.

\dfrac{1}{y} = \dfrac{1}{10\,\mathrm{cm}} - \dfrac{1}{15\,\mathrm{cm}} = \dfrac{1}{30\,\mathrm{cm}}, \quad y = 30\,\mathrm{cm}

LaTeX commands in this formula

\dfrac: fraction (display)

How to use this formula in LaTeX?

Copy the code with the button above - $$…$$ is centered display math.
Paste it into the CamteX editor, Overleaf or any LaTeX document.
Inside a sentence, use single $…$ instead of double.
The formula needs the amsmath package - CamteX templates include it in the preamble.

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