A group of students wishes to investigate the circumstances under which reflections from a plane mirror can be treated using geometric optics. They have a broadband white-light source, an adjustable circular aperture of variable diameter d, a front-surface mirror of fixed size, and a movable screen that can be placed at different distances from the mirror.
(a) Identify the independent variable the students should vary and the dependent variable they should measure in order to study the transition from geometric reflection to diffraction-dominated behavior.
(b) Outline a step-by-step experimental procedure—no more than four major steps—that would allow the students to collect the necessary data.
(c) Describe the qualitative trend you expect for the measured width of the reflected spot on the screen as a function of aperture diameter, and explain the physical reasoning behind this trend.
(d) Discuss how the results of this experiment would inform the design of optical instruments that rely on mirrors, such as periscopes or astronomical telescopes.