In a game of "Clue," Ms. White is killed in the...

In a game of "Clue," Ms. White is killed in the conservatory. A spectrometer in each room records who is present to help find the murderer. For example, if someone wearing yellow is in a room, light at $580 \mathrm{nm}$ is reflected. The suspects are Col. Mustard, Prof. Plum, Mr. Green, Ms. Peacock (blue), and Ms. Scarlet. At the time of the murder, the spectrometer in the dining room shows a reflection at $520 \mathrm{nm},$ those in the lounge and the study record lower frequencies, and the one in the library records the shortest possible wavelength. Who killed Ms. White? Explain.

Key Concepts

Wavelength-Frequency Relationship

There is an inverse relationship between wavelength and frequency in light; as the wavelength decreases, the frequency increases. This fundamental principle helps in associating a detected wavelength with its relative position in the color spectrum. For example, a spectrometer reading of a shorter wavelength indicates a color towards the violet end of the spectrum, while a longer wavelength points to colors like red or yellow.

Deductive Reasoning from Physical Evidence

Deductive reasoning from physical evidence involves using measured properties — in this case, wavelengths of reflected light — to logically infer the identity or presence of specific individuals, based on the known correlations between colors and suspects. By matching the observed wavelengths to the known color assignments of the suspects’ attire, one can eliminate possibilities and ultimately identify the individual whose measured wavelength, such as the one corresponding to the shortest wavelength (i.e. highest frequency color), implicates them in the scenario.

Spectrometry

Spectrometry is the scientific technique used to measure and analyze light by its wavelength and frequency. In general, spectrometers are used to detect which wavelengths of light are present in a sample, providing a ‘fingerprint’ that can identify substances or, in investigative puzzles, can correlate the observed wavelengths to specific sources or colors.

Visible Light Spectrum

The visible light spectrum is the portion of the electromagnetic spectrum that human eyes can perceive, typically ranging from about 400 nm (violet) to 700 nm (red). Each color in this range corresponds to a specific segment of wavelengths, allowing for identification of colors by their wavelength. For instance, green light is around 520 nm, blue light typically is between 450 nm and 495 nm, and purple or violet light is at the lower end, around 400 nm.

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