The smallest difference in wavelength that can be measured for electromagnetic radiation depends on various factors, including the experimental setup and the sensitivity of the measuring instruments.
In principle, according to the wave-particle duality of quantum mechanics, electromagnetic radiation can be described as both waves and particles (photons). From a wave perspective, the wavelength represents the distance between successive wave crests or troughs.
The accuracy and precision of measuring the difference in wavelength can be limited by the experimental setup and the properties of the radiation being measured. The key factor is the resolving power of the measurement apparatus, which determines its ability to distinguish between closely spaced wavelengths.
In general, the resolving power of a measurement apparatus, such as a spectrometer, is determined by its design, the quality of its components (such as diffraction gratings or prisms), and the characteristics of the radiation being measured (e.g., its frequency range, intensity, coherence, etc.).
State-of-the-art scientific instruments can achieve extremely high resolving powers, enabling the measurement of very small differences in wavelength. For example, advanced spectroscopic techniques, such as those used in laser spectroscopy or high-resolution imaging, can achieve wavelength resolutions in the range of picometers (10^(-12) meters) or even smaller.
It's worth noting that the uncertainty principle in quantum mechanics places a fundamental limit on simultaneous measurements of certain pairs of properties, such as position and momentum, or energy and time. This principle implies that there is always some inherent uncertainty or limit in the simultaneous measurement of certain properties, including wavelength and frequency.
In summary, the smallest difference in wavelength that can be measured for electromagnetic radiation depends on the resolving power of the measurement apparatus and the specific techniques used. Advanced instruments can achieve high resolving powers, allowing for the measurement of very small differences in wavelength, often in the picometer range or smaller.