Question #43223

This question tests the invariance of fringe width under geometric scaling and the breakdown of the paraxial approximation.

Students often blindly apply the standard YDSE formula $\beta = \lambda D/d$, treating $D$ as the distance to the screen and $d$ as some effective source separation (leading to distractors like $4\lambda/3$ or $2\lambda/3$).

However, the biprism severely refracts the rays (non-paraxial, $\delta = 30^\circ$), creating two intersecting plane waves.

The true fringe width is a local property of the intersecting waves, given by $\beta = \lambda / (2 \sin\delta)$, which is independent of the screen distance $D$.

Using the geometric $D$ and $d$ fails because the effective virtual sources are shifted differentially by the large aberration (non-small angle refraction), making the small-angle approximation $\sin\theta \approx \tan\theta$ invalid.