Diffraction

Diffraction is the bending and spreading of waves around obstacles or through openings. When the opening size is comparable to the wavelength, the effect becomes dramatic.

Single-Slit Diffraction

For a slit of width $a$ illuminated by monochromatic light of wavelength $\lambda$, dark fringes (minima) appear at angles satisfying:

$a \sin\theta = m\lambda \quad m = \pm 1, \pm 2, \ldots$

The first minimum (smallest angle) occurs at:

$\sin\theta = \frac{\lambda}{a}$

$\theta = \arcsin\!\left(\frac{\lambda}{a}\right)$

The central bright maximum has width $2\theta$ — it is twice as wide as the other maxima.

Example: $\lambda = 500\,\text{nm}$, $a = 100\,\mu\text{m}$:

$\theta = \arcsin\!\left(\frac{500 \times 10^{-9}}{100 \times 10^{-6}}\right) = \arcsin(0.005) \approx 0.287°$

Diffraction Grating

A diffraction grating has thousands of slits per millimeter. For grating spacing $d$ (distance between adjacent slits), bright maxima occur at:

$d \sin\theta = m\lambda \quad m = 0, \pm 1, \pm 2, \ldots$

Solving for the angle of the $m$-th order maximum:

$\theta = \arcsin\!\left(\frac{m\lambda}{d}\right)$

Diffraction gratings are used in spectrometers to separate light into its component wavelengths with high precision.

Example: $\lambda = 550\,\text{nm}$, $d = 2\,\mu\text{m}$ (500 lines/mm), $m = 1$:

$\theta = \arcsin\!\left(\frac{550 \times 10^{-9}}{2 \times 10^{-6}}\right) = \arcsin(0.275) \approx 15.96°$

Your Task

Implement the two angle formulas. Use math.asin and math.degrees. Wavelengths are in nm; slit widths/spacings are in micrometers ($\mu$m).