A miniature spectrometer used for chemical analysis has a diffraction grating wi

Question

A miniature spectrometer used for chemical analysis has a diffraction grating with800 slits/mm set 25.0 mm in front of the detector "screen." The detector can barely distinguish two bright lines that are 30 m apart in the first-order spectrum.

What is the resolution of the spectrometer at a wavelength of 600 nm ? That is, if two distinct wavelengths can barely be distinguished, one of them being 600 nm , what is the wavelength difference between the two?

Express your answer to two significant figures and include the appropriate units.

There are a TON of this same question on Chegg already. I've tried the formulas on all of them and can not get the right answer.

Explanation / Answer

given,

numbers of slit per mm = 800

or slit width = 1/800 mm

distance of screen = 25 mm

for light of wavelength 600 nm

y1 = m1 * wavelength * D / d

resolution = y2 - y1

resolution = m2 * wavelength * D / d - m1 * wavelength * D / d

resolution = (m2 - m1) * (wavelength * D / d)

resolution = (2 - 1) * (600 * 10^-9 * 25 * 10^-3 / (10^-3/800))

resolution = 0.012 m

if resolution = 30 * 10^-6 m

30 * 10^-6 = 1 * * 25 * 10^-3 / (10^-3/800)

= 1.5 * 10^-9 m

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