Thermal-imaging engineers are designing a sensor optimized to detect objects whose…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
Thermal-imaging engineers are designing a sensor optimized to detect objects whose thermal emission is strongest near a wavelength of λtarget=10.0μm. For reliable operation, the sensor must register at least 90 % of its maximum response, which occurs when the object’s peak emission wavelength lies within ±15% of λtarget. Assume all objects of interest behave as perfect thermal emitters.
(a) Determine the precise object temperature at which the peak of the emission spectrum is exactly λtarget=10.0μm. Provide your answer in kelvin.
(b) Calculate the temperature range (minimum to maximum) over which the sensor will register at least 90 % of its maximum response, given the ±15% tolerance on λtarget.
(c) An engineer proposes to calibrate the sensor using a laboratory blackbody cavity whose temperature can be varied between 250K and 600K. Explain whether this temperature span is sufficient to perform the full calibration required in part (b). Support your answer with quantitative reasoning.
(d) Suppose manufacturing variations limit the sensor’s useful wavelength window to 8.0μm–12.0μm. Discuss how this narrower window would modify the acceptable temperature range you calculated in part (b). No additional arithmetic is required; focus on the qualitative implications.