how do you calculate the wavelength of light? For chemsitry lab, we calibrated the scale reading of Hg, for example, to be 4.91 cm which is violet and the given wavelength says 436. For Hg, it says scale reading of 5.51 cm for green and wavelength of 546. But for overhead fluorescent, I took the scale reading of 4.93 for violet but don't know how to calculated the wavelength. Any help with steps shown would be great!
Well, the equipment appears to be giving you the wavelength; however, the scale seems to be skewed (off-calibration) so you have to correct for it.
The scale readings you give appear to be off a few orders of magnitude; the wavelengths you list as "given wavelengths" are in nanometers. Wavelengths of 4-5 centimeters as your measurements suggest would place the emission spectra in the "ELF" radio frequency range at the extreme low end of detectable electromagnetic spectra, and well out of the range of visible light. So, just for the sake of argument, let's say you interpreted the measurements incorrectly, and these numbers should be in the hundreds and represent nanometers of wavelength (or, as written, they represent tenths of a micrometer).
Given that assumption, the numbers are still off a bit, indicating the instrument is slightly out of calibration. If the instrument itself isn't adjustable to correct the values, "calibrating" it boils down to a percentage error calculation that is then applied to further readings: (experimental-theoretical)/theoretical * 100%. For your violet wavelength, you got 491nm but expected 436. That is (491-436)/436 * 100% = 12.6% error. The green wavelength reading was 551 when you expected 546; those two are much closer (0.915% error), which indicates that the equipment you're using has some chromatic aberration. That's understandable in an instrument designed to "fracture" light into a prismatic spectrum; other light-sensing equipment, like cameras, generally try to minimize it so all the wavelengths emanating from one point on the subject pass through the lens to expose one point on the film or photocell. But I digress.
Your violet spectral line reading off of an ordinary fluorescent lamp is 493nm. Given the percentage error measures on this end of the scale, this reading is about 12.6% too high; so, we divide by 112.6% to get the actual measured wavelength of 437.8. That measurement, against the known emission spectra of mercury vapor, has a percentage error of only (437.8-436)/436 * 100% = 0.42%, which for a measurement made with classroom lab equipment and other less-than-ideal conditions is pretty darn close.