Young's two slits turn a wavelength far too small to see into fringes millimeters apart, as in Double-Slit Interference. Exam problems then change one thing (the light, the slits, the medium) and ask what moves. Each problem here is one short scene and a chain of questions. Answer them in order: each later question uses what you found before, so a slip early on carries through. Keep full precision between steps and round only at the end.
Key idea
Bright fringes: $d\sin\theta = m\lambda$. For small angles, $$y_m = m\frac{\lambda L}{d}, \qquad \Delta y = \frac{\lambda L}{d}.$$ Dark fringes sit halfway between. In a medium of index $n$ the wavelength, and so the spacing, is divided by $n$.
Worked example: Fringe spacing
Light of $600\ \text{nm}$ passes slits $0.30\ \text{mm}$ apart onto a screen $1.5\ \text{m}$ away. Find (1) the fringe spacing and (2) the distance to the second dark fringe.
- (1) $\Delta y = \dfrac{(600 \times 10^{-9})(1.5)}{0.30 \times 10^{-3}} = 3.00\ \text{mm}$.
- (2) The second dark fringe is at $1.5\,\Delta y = 4.50\ \text{mm}$.
Answer: $3.00\ \text{mm}$, $4.50\ \text{mm}$
Common mistake
Counting dark fringes like bright ones: the first dark fringe is at $\tfrac{1}{2}\Delta y$, not $\Delta y$. Check: there is a bright fringe at the center, so dark ones must be offset from it.