Optics & Light Cheat Sheet

A printable reference covering reflection, refraction, Snell’s law, lenses, mirrors, magnification, and light wave behavior for grades 10-11.

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Optics is the study of light and how it behaves when it travels, reflects, refracts, and forms images. Students need this cheat sheet to connect ray diagrams with the equations used for mirrors, lenses, and waves. It is especially useful for solving problems involving focal length, image distance, magnification, and the speed of light in materials. Clear formulas and sign rules help prevent common errors in multi-step optics questions. The most important ideas include the law of reflection, Snell’s law, the thin lens and mirror equation, and the magnification equation. Light travels at speed $c = 3.00 \times 10^8\,\text{m/s}$ in a vacuum, but slows down in materials according to the index of refraction $n = \frac{c}{v}$ . Images can be real or virtual, upright or inverted, and enlarged or reduced depending on object position and optical device. Ray diagrams and formulas should always agree with each other.

Key Facts

The law of reflection states that the angle of incidence equals the angle of reflection, so $\theta_i = \theta_r$ .
The index of refraction is $n = \frac{c}{v}$ , where $c$ is the speed of light in a vacuum and $v$ is the speed of light in the material.
Snell’s law relates refraction angles by $n_1\sin\theta_1 = n_2\sin\theta_2$ .
The mirror and thin lens equation is $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$ .
Linear magnification is $m = \frac{h_i}{h_o} = -\frac{d_i}{d_o}$ .
Wave speed, frequency, and wavelength are related by $v = f\lambda$ .
For total internal reflection, the critical angle satisfies $\sin\theta_c = \frac{n_2}{n_1}$ when $n_1 > n_2$ .
A converging lens has positive focal length $f > 0$ , while a diverging lens has negative focal length $f < 0$ .

Vocabulary

Ray: A ray is a straight-line model showing the direction that light travels.
Normal: The normal is an imaginary line perpendicular to a surface at the point where a light ray strikes.
Refraction: Refraction is the bending of light as it changes speed when moving from one medium into another.
Focal Length: Focal length is the distance from a mirror or lens to the focal point, represented by $f$ .
Real Image: A real image forms where light rays actually meet and can be projected onto a screen.
Virtual Image: A virtual image forms where light rays appear to come from but do not actually meet.

Common Mistakes to Avoid

Measuring angles from the surface instead of the normal is wrong because reflection and refraction angles are always measured from the normal line.
Using Snell’s law without matching each angle to its medium is wrong because $n_1\sin\theta_1 = n_2\sin\theta_2$ depends on the correct side of the boundary.
Forgetting sign conventions in $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$ can give the wrong image type, especially for virtual images and diverging lenses.
Treating frequency as changing during refraction is wrong because frequency stays constant when light enters a new medium, while speed and wavelength change.
Ignoring the negative sign in $m = -\frac{d_i}{d_o}$ is wrong because the sign tells whether the image is upright or inverted.

Practice Questions

1 Light travels from air with $n_1 = 1.00$ into glass with $n_2 = 1.50$ at an incident angle of $30.0^\circ$ . Find the angle of refraction using $n_1\sin\theta_1 = n_2\sin\theta_2$ .
2 An object is placed $20.0\,\text{cm}$ from a converging lens with focal length $10.0\,\text{cm}$ . Use $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$ to find the image distance.
3 A light wave has frequency $5.00 \times 10^{14}\,\text{Hz}$ in a vacuum. Find its wavelength using $c = f\lambda$ and $c = 3.00 \times 10^8\,\text{m/s}$ .
4 Explain why a straw appears bent when placed in water, using the ideas of changing light speed, refraction, and the normal line.