Interference, Diffraction, and Polarization (4D) Practice Test

A microfluidic cytometry device uses a 532-nm laser to illuminate a double-slit mask placed immediately before a detector. The two slits are separated by $d = 0.20\ \text{mm}$, and the detector screen is $L = 1.5\ \text{m}$ from the mask. The device is calibrated in air ($n \approx 1.00$). Assume small-angle conditions so that $y_m \approx m\lambda L/d$. Which observation is most consistent with the described interference pattern when the slits are illuminated uniformly?

Constants: $\lambda = 532\ \text{nm}$; $1\ \text{nm} = 10^{-9}\ \text{m}$.

In an ophthalmic instrument, a 633-nm HeNe laser passes through a single rectangular slit of width $a = 0.10\ \text{mm}$ to produce a diffraction pattern on a sensor located $L = 2.0\ \text{m}$ away. The first diffraction minima satisfy $\sin\theta \approx \lambda/a$ (small angles), and the half-width of the central maximum on the screen is $y_1 \approx L\tan\theta \approx L\sin\theta$. How would doubling the slit width to $0.20\ \text{mm}$ affect the diffraction pattern?

Constants: $\lambda = 633\ \text{nm}$.