Common Pitfalls

Confusing Fraunhofer and Fresnel diffraction. Fraunhofer (far-field) patterns are Fourier transforms; Fresnel (near-field) patterns involve Fresnel integrals. The transition occurs at $R \sim a^2/\lambda$.

Ignoring the phase in interference calculations. Phase differences determine constructive and destructive interference. Always track the optical path length carefully.

Misidentifying Brewster”s angle. Brewster’s angle is for the reflected beam, not the transmitted beam. At Brewster’s angle, the reflected light is purely $s$-polarised.

Neglecting the difference between intensity and amplitude. Interference patterns depend on amplitudes (add with phases), while intensities add without phases for incoherent sources. The visibility of fringes is determined by the coherence of the source.

Forgetting that the Airy pattern involves $J_1$Not $J_0$. The first zero of $J_1(x)$ is at $x = 3.832$Not at $x = 2.405$ (which is the first zero of $J_0$).