A thin acrylic film (index nfilm=1.50) is sandwiched between air on top and a rigid plastic substrate with index nsub=1.60 below. The thickness t of the film is chosen so that, for normal incidence,
• green light with wavelength 540nm in air is transmitted most strongly (minimal reflection), while
• red light with wavelength 630nm in air is reflected most strongly (maximal reflection).
Assume the only significant reflected rays are those from the top and bottom surfaces of the film.
(a) For each of the two interfaces (air–film and film–substrate), indicate whether the reflected light undergoes a half-wavelength phase shift. Justify your answers based on index comparisons.
(b) Write the interference conditions that must be satisfied for (i) minimal reflection of the 540nm light and (ii) maximal reflection of the 630nm light in this three-medium system. Clearly define any interference order numbers you introduce.
(c) Determine the smallest film thickness t that simultaneously meets both interference conditions by selecting appropriate integer orders. Show all algebraic steps and give the final thickness to the nearest nanometer.
(d) Using the thickness found in part (c), discuss qualitatively whether blue light with wavelength around 460nm is more likely to be reflected or transmitted, and explain your reasoning.