Waves and optics

Snell's law - formula in LaTeX

Describes how light bends at the boundary between two media. Both angles are measured from the normal to the surface, not from the surface itself. Write \sin with a backslash: plain sin is treated as a product of three variables.

n_1\sin\theta_1 = n_2\sin\theta_2

LaTeX code

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$$
n_1\sin\theta_1 = n_2\sin\theta_2
$$

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What the symbols mean

$n_1, n_2$: refractive indices of the two media
$\theta_1$: angle of incidence
$\theta_2$: angle of refraction

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

Worked example

A light ray passes from air (n = 1) into water (n = 1.33) at 45°. The function name comes from \sin; a bare sin is typeset as the product of three variables s, i and n.

\sin\theta_2 = \dfrac{n_1}{n_2}\sin\theta_1 = \dfrac{1}{1.33}\sin 45^\circ \approx 0.532, \quad \theta_2 \approx 32.1^\circ

LaTeX commands in this formula

x_{0}: subscript; wrap several characters in braces
\sin: sine function in upright type
\theta: Greek letter theta

How to use this formula in LaTeX?

Copy the code with the button above - $$…$$ is centered display math.
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The formula works without extra packages.

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