Two continuous-wave laboratory lasers operate steadily at the same radiant output power of 2.0mW. Laser A emits light of wavelength 405nm (violet) and Laser B emits light of wavelength 810nm (near-infrared).
A student investigates how the choice of wavelength affects the rate at which photons are emitted.
(a) Explain qualitatively how the wavelength of the emitted light influences the energy carried by each individual photon.
(b) Derive an algebraic expression for the ratio NANB of photon emission rates for Lasers B and A in terms of their respective wavelengths.
(c) Calculate the numerical value of NANB using the given wavelengths. Show all work and include units with your final answer.
(d) Discuss what this ratio implies about the relative numbers of photons that must arrive at the human eye for the two beams to deliver the same optical power, and comment on one practical consequence for designing detectors or communication systems that operate at longer wavelengths.