Mistake 1: Confusing dark fringe numbering The $n$th dark fringe formula $y_n = (2n-1)\lambda D/(2d)$ starts at $n = 1$, NOT $n = 0$. The 1st dark fringe is at $\beta/2$, the 2nd at $3\beta/2$, and so on. Using $n = 0$ in the dark fringe formula gives $y = -\lambda D/(2d)$, which is nonsensical. Always write out the formula and substitute carefully.

Mistake 2: Forgetting that fringe width decreases in a denser medium Students often think immersing YDSE in water increases fringe width because water slows light. The opposite is true: fringe width $\beta = \lambda D/d$ uses the wavelength in the medium, which is $\lambda/n < \lambda$. Fringe width decreases by factor $n$.

Mistake 3: Applying Malus's law to unpolarized light Malus's law $I = I_0\cos^2\theta$ applies only to already-polarized incident light. The first polaroid in any sequence converts unpolarized light to polarized at half intensity ($I_0 \to I_0/2$). Applying $\cos^2\theta$ to the original unpolarized beam is wrong.

Mistake 4: Ignoring the $\lambda/2$ phase shift at the denser medium This is relevant for thin film problems (beyond core NEET). In YDSE there is no such shift, but for polarization questions, students sometimes incorrectly apply a path difference where only an angle matters.

Mistake 5: Treating single slit minima the same as YDSE bright fringe condition Single slit MINIMA: $a\sin\theta = n\lambda$ (same algebraic form as YDSE BRIGHT fringes). This symmetry is a notorious trap. In YDSE, $d\sin\theta = n\lambda$ gives BRIGHT fringes; in single slit, $a\sin\theta = n\lambda$ gives DARK fringes (minima). The physical setups are different; the conditions are opposite in implication.