Imagine that you are playing a game of clue in which mrs. white is killed in the conservatory. you have a device in each room to you find the murderer: a spectrometer that detects the entire visible spectrum to indicate who is in that room. for example, if someone wearing yellow is in a room, light at 580 nm is reflected. the suspects are colonel mustard, professor plum, mr. green, mrs. peacock (blue), and miss scarlet. at the time of the murder, the spectrometer in the dining room recorded a reflection at 520 nm. the spectrometry in the lounge and study recorded reflections of lower frequencies, and the one in the library recorded a reflection of the second shortest wavelength of the five recorded. who killed mrs. white

Explanation:

1) Wavelengths for the different light colors (visible light) and related character:

Color  Wavelength          related character

Violet  380–450 nm  ← Professr Plum

Blue  450–485 nm  ← Mrs. Peacock

Cyan  485–500 nm  

Green  500–565 nm  ← Mr. Green

Yellow  565–590 nm  ← Colonel Mustard

Orange  590–625 nm  

Red  625–740 nm  ← Miss Scarlet

2) At the time of the murder, the spectrometers recorded:

a) In the dining room: 520 nm.

520 nm is in the range 500 - 565 nm, which is the range for green color, so Mr. Green was in the dining room and is no more a suspect.

b) In the lounge and study: lower frequencies.

Since frequency and wavelength are inversely related, the wavelengths in the longe and study have to be of yellow and red colors, which are the only two with longer wavelengths from the option given.

Then, Mustard and Scarlet are not criminal.

c) In the library: the second shortest wavelength of the five recorded.

The second shortest wavelength, as per the table, is that of blue color. So, Mrs. Peacock is not the killer.

The only left option is violet, so Mr. Plum is the only who could be at the conservatory and he is the killer.