Q.In a two-slit interference experiment using light of wavelength $\lambda=6000\ \text{\AA}$, state whether a bright or a dark fringe is formed at a point where the path difference between the two interfering waves is

Given $\lambda=6000\ \text{\AA}=6\times10^{-7}\ \text{m}=0.6\ \mu\text{m}$.

1. Path difference $\Delta=1.8\ \mu\text{m}$. Expressing this as a multiple of $\lambda$:

   $\frac{\Delta}{\lambda}=\frac{1.8}{0.6}=3$

   an exact integer, so $\Delta=3\lambda$, satisfying the bright-fringe condition $\Delta=n\lambda$ with $n=3$ -- a bright fringe is formed.
2. Path difference $\Delta=1.5\ \mu\text{m}$:

   $\frac{\Delta}{\lambda}=\frac{1.5}{0.6}=2.5$

   an exact half-integer, so $\Delta=2.5\lambda=(2+\tfrac12)\lambda$, satisfying the dark-fringe condition $\Delta=(n+\tfrac12)\lambda$ with $n=2$ -- a dark fringe is formed.
   ✓Final answer

   1. $1.8\ \mu\text{m}=3\lambda$ -- bright fringe.
   2. $1.5\ \mu\text{m}=2.5\lambda$ -- dark fringe.

Express the given path difference as a multiple of $\lambda$ and check whether it is an integer (bright) or a half-integer (dark).

• Forgetting to convert $\lambda$ from angstroms to micrometres (or both quantities to the same unit) before dividing.
• Misclassifying a half-integer multiple as bright instead of dark, or vice versa.