An optical instrument contains two thin interference filters arranged in series along the beam path of an incident white-light source.
• Filter 1 transmits all wavelengths shorter than 540 nm and blocks longer wavelengths.
• Filter 2, placed immediately after Filter 1, transmits all wavelengths longer than 480 nm and blocks shorter wavelengths.
Light that passes both filters is then sent to a photodetector for measurement.
(a) Determine the numerical wavelength range that ultimately reaches the photodetector after passing through both filters.
(b) Identify the principal color (or combination of colors) that the detector will register, and explain how you arrived at your answer.
(c) The instrument designer wants to adjust the system so that only a narrow, visually "pure" green band (centered near 525 nm with a width of ±10 nm) reaches the detector. Propose a specific modification to one or both filters that would achieve this goal, and justify how your proposal accomplishes the desired spectral selection.