Question #94466

A parallel beam of monochromatic light of wavelength $\lambda$ is incident normally on an opaque screen containing two identical parallel slits. Each slit has a width $a$ and the center-to-center separation between the slits is $d$ (where $d > a$). A transparent dielectric slab of refractive index $\mu$ and uniform thickness $t$ is placed directly over the upper slit. The resulting interference-diffraction pattern is observed on a distant screen. The thickness $t$ is gradually increased from zero until the zeroth-order central interference maximum is completely suppressed because it coincides exactly with the first minimum of the diffraction envelope. (The Rayleigh criterion for resolution is closely related to the angular position of this first diffraction minimum). Assuming the angle of diffraction $\theta$ is small, determine the required thickness $t$ of the slab, and the angular shift $\Delta \theta_{\text{diff}}$ of the central maximum of the diffraction envelope from the optical axis for any general thickness $t$. All lengths are in meters and angles in radians. Which of the following correctly represents the pair $(t, \Delta \theta_{\text{diff}})$?