Question #43734

A single slit of width $a = 0.10 \text{ mm}$ is placed parallel to a perfectly reflecting flat optical mirror. The center of the slit is at a height $h = 0.30 \text{ mm}$ above the mirror. The slit is illuminated normally by monochromatic light of wavelength $\lambda = 600 \text{ nm}$. A screen is placed at a large distance $D = 2.0 \text{ m}$ from the slit, perpendicular to the mirror. The intensity distribution on the screen for $y > 0$ (where $y=0$ is the intersection of the mirror plane with the screen) is a combined effect of single-slit diffraction and interference between the direct wave and the reflected wave. Assume the small angle approximation is valid. How many interference maxima are observed on the screen strictly within the central diffraction envelope (i.e., between $y = 0$ and the first diffraction minimum)?