AIIMS 2019 Physics Interference MCQ Question

The calculation for the distance to the 5th dark fringe in a double-slit interference pattern is derived from the formula $y = \frac{(m + 0.5) \lambda D}{d}$, where $m$ is the fringe order, $\lambda$ is the wavelength, $D$ is the distance to the screen, and $d$ is the slit separation. Substituting the given values into the equation $\frac{9 \lambda D}{2d} = 4 \times 10^{-3}$ leads to $d = 1.35 \, \text{mm}$, confirming option A as correct. The other options (1.45 mm, 1.55 mm, and 1.65 mm) do not satisfy the derived equation, indicating they do not correspond to the correct slit separation for the specified fringe distance.