Optics Geometric, Wave, and Quantum Cheat Sheet

Key Facts

• The law of reflection states that the incident angle equals the reflected angle, so $\theta_i = \theta_r$ measured from the normal.
• Snell's law relates refraction at an interface by $n_1\sin\theta_1 = n_2\sin\theta_2$.
• The thin lens and mirror equation is $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$, with magnification $m = -\frac{d_i}{d_o} = \frac{h_i}{h_o}$.
• For a single slit of width $a$, diffraction minima occur when $a\sin\theta = m\lambda$ for $m = 1,2,3,\ldots$.
• For double-slit interference with slit separation $d$, bright fringes occur when $d\sin\theta = m\lambda$ and dark fringes occur when $d\sin\theta = \left(m + \frac{1}{2}\right)\lambda$.
• Malus's law gives transmitted intensity through a polarizer as $I = I_0\cos^2\theta$.
• Photon energy and momentum are $E = hf = \frac{hc}{\lambda}$ and $p = \frac{h}{\lambda}$.
• The Rayleigh resolution criterion for a circular aperture is $\theta_{\min} = 1.22\frac{\lambda}{D}$.

Vocabulary

Geometric optics

The model of light that treats light as rays traveling in straight lines except when reflecting or refracting.

Index of refraction

A material property defined by $n = \frac{c}{v}$ that tells how much light slows in a medium.

Interference

The addition of overlapping waves that can produce constructive or destructive intensity patterns.

Diffraction

The spreading of waves around edges or through openings, most noticeable when the opening size is comparable to $\lambda$.

Polarization

The orientation of the electric field oscillation in a light wave.

Photon

A quantum of electromagnetic radiation with energy $E = hf$ and momentum $p = \frac{h}{\lambda}$.