A front-surface plane mirror has an isolated scratch that exposes a narrow linear strip of reflective material of width a=0.10mm running vertically down the center of the otherwise perfectly absorbing mirror. A red He–Ne laser (λ=632nm) shines perpendicularly onto the mirror, completely covering the scratch as well as the surrounding absorbing area. A viewing screen is placed a distance D=5.0m in front of the mirror.
(a) Without performing detailed calculations, sketch the qualitative intensity distribution you expect to observe on the screen and briefly describe its main features.
(b) Derive an expression for the transverse positions ym of the intensity minima on the screen in terms of the order number m, the wavelength λ, the strip width a, and the distance D.
(c) Calculate the distance on the screen between the central maximum and the first minimum (m=±1).
(d) Explain why a purely geometric‐optics (ray) analysis would fail to predict the pattern found in part (a). State how the result would change if the strip width a were increased to 10mm while all other parameters remained the same.