Diffraction grating

Same condition as the double slit, with $d$ the spacing between neighbouring slits and $m = 0, 1, 2, \ldots$ the order. The sheet prints $\Delta D = d\sin\theta$ and $\Delta D = m\lambda$; there is no separate grating equation to look up.

What the extra slits buy is sharpness, not new positions. With two slits the intensity falls off gently between maxima. With thousands, light from all of them agrees only in a very narrow angular window, and misses elsewhere, so the maxima collapse into thin bright lines with darkness in between. That is why a grating can separate two wavelengths a double slit would blur together.

If a grating is specified as lines per millimetre, invert it: 600 lines per mm gives $d = 1/600$ mm, or about $1.67 \times 10^{-6}$ m.

Do not use the small-angle approximation here. The conventions block on the AP Physics 2 sheet states it for single- and double-slit diffraction. A grating's spacing is only a few wavelengths, so its first order can sit at tens of degrees, and $\sin\theta \approx \tan\theta$ fails.

White light. The centre maximum stays white, because $m = 0$ puts every wavelength at $\theta = 0$. Every higher order fans out into a spectrum, and since $\sin\theta$ grows with $\lambda$, red lands farthest from the centre and violet closest. Topic 14.8 works the numbers.