Geometric and Wave Optics Cheat Sheet

Key Facts

• The law of reflection is $\theta_i = \theta_r$, where both angles are measured from the normal line.
• Snell’s law is $n_1 \sin \theta_1 = n_2 \sin \theta_2$, where $n$ is the index of refraction.
• The speed of light in a medium is $v = \frac{c}{n}$, so a larger $n$ means light travels more slowly.
• The thin lens and mirror equation is $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$, where $f$ is focal length, $d_o$ is object distance, and $d_i$ is image distance.
• Magnification is $m = \frac{h_i}{h_o} = -\frac{d_i}{d_o}$, where a negative value means the image is inverted.
• For a double slit, bright fringes occur when $d \sin \theta = m\lambda$ and dark fringes occur when $d \sin \theta = \left(m + \frac{1}{2}\right)\lambda$.
• For a single slit, diffraction minima occur when $a \sin \theta = m\lambda$, where $m = 1, 2, 3, \ldots$.
• Malus’s law for polarized light is $I = I_0 \cos^2 \theta$, where $\theta$ is the angle between the light’s polarization direction and the polarizer axis.

Vocabulary

Index of refraction

The index of refraction $n$ is a measure of how much a medium slows light, defined by $n = \frac{c}{v}$.

Focal length

Focal length $f$ is the distance from a lens or mirror to the point where parallel incoming rays converge or appear to diverge.

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 only appear to come from and cannot be projected onto a screen.

Interference

Interference is the combining of waves, producing brighter regions by constructive interference and darker regions by destructive interference.

Diffraction

Diffraction is the bending and spreading of waves when they pass through an opening or around an obstacle.