A monochromatic beam of light with wavelength 520 nm passes through a narrow rectangular slit and forms a single-slit diffraction pattern on a distant screen. In a second trial, the same beam is directed through an otherwise identical slit whose width has been reduced to one-half of the original value.
Compare the diffraction patterns produced in the two trials.
(1) Predict how the angular position of the first minimum will change when the slit width is halved. State whether the angle increases, decreases, or remains the same, and support your prediction qualitatively by referring to the relationship among slit width, wavelength, and diffraction angle.
(2) Describe how the overall spacing between successive dark fringes (minima) will differ between the two trials. Explain your reasoning.
(3) For each trial, discuss whether the small-angle approximation sinθ≈θ (in radians) is likely to be valid for locating the first minimum. Support your conclusion without performing a detailed numerical calculation.