The diffraction grating — common mistakes

Always remember to convert all units to SI (metres for $d$ and $\lambda$) before applying the formula. The grating spacing $d$ is the reciprocal of the number of lines per metre. Pay close attention to the number of lines per millimetre, as this requires a calculation to find $d$. Also, clearly state the value of 'n' you are using, especially when calculating the maximum possible order, which must be an integer.

Both split white light into a spectrum. However, a prism does this through dispersion (different refractive indices for different wavelengths), while a diffraction grating does so via diffraction and interference. Gratings generally produce a much wider, more distinct, and more angularly separated spectrum, with angles depending on wavelength and grating spacing, not the prism material's refractive index.

Coherent light ensures that the waves passing through different slits maintain a constant phase relationship and have the same frequency. Without coherence, the phase differences at any point on the screen would fluctuate randomly, leading to rapidly changing interference conditions. This would result in an unstable and unobservable pattern, or merely a general blurring of light, not distinct bright and dark fringes.

The maximum number of orders ($n_{max}$) is limited by the physical constraint that $\sin \theta cannot exceed 1$. Therefore, for any order $n$ where the ratio $n\lambda/d$ is greater than 1, no real angle $\theta exists for that maximum$, and it will not be observed. You can find $n_{max}$ by setting $\sin \theta = 1 in the grating equation and solving for$n$$, then taking the integer part of the result.

Yes, they can, especially at higher orders. For example, the third-order maximum for a shorter wavelength (like violet) might appear at the same angle as the second-order maximum for a longer wavelength (like red). This can be checked using the condition n₁λ₁ = n₂λ₂. This overlapping is a key difference from the single, non-overlapping spectrum produced by a prism.