Fringe that will fall on a 400-nm dark fringe, and what are the fringes\' corres

Question

Fringe that will fall on a 400-nm dark fringe, and what are the fringes' corresponding orders? On the screen of a multiple-slit system, the interference pattern shows bright maxima separated by 0.86 degree and seven minima between each bright maximum. (a) How man y slits are there? (b) What's the slit separation if the incident light has wavelength 656.3 nm? You're designing a spectrometer whose specifications call for a minimum of 5 degree separation between the red hydrogen-alpha line at 656 nm and the yellow sodium line at 589 nm when the two are observed in third order with a grating spectrometer. Available gratings have 2500 lines/cm, 3500 lines/cm, or 4500 lines/cm. What's the coarsest grating you can use? For visible light with wavelengths from 400 nm to 700 nm, show that the first-order spectrum is the only one that doesn't overlap with the next higher order. Find the total number of lines in a 2.5-cm-wide diffraction grating whose third-order spectrum puts the 656-nm hydrogen spectral line 37 degree from the central maximum. What order is necessary to resolve 647.98-nm and 648.07-n spectral lines using a 4500-line grating? A thin film of toluene (n = 1.49) floats on water. Find the

Explanation / Answer

The formula to use for diffraction grating is dsin = m

You will need the angles for both wavelengths, and then subtract to see if you get 5o

For the 2500 lines/cm (or 250000 lines/m)

d = 1/250000 = 4 X 10-6 m

sin = (3)(656 X 10-9)/(4 X 10-6)     = 29.47o

sin = (3)(589 X 10-9)/(4 X 10-6)     = 26.22o

The difference is only 3.25o so 2500 lines per cm is out - Can't be used

Lets try 3500 lines/cm (or 350000 lines/m)

d = 1/350000 = 2.857 X 10-6 m

sin = (3)(656 X 10-9)/(2.857 X 10-6)     = 43.54o

sin = (3)(589 X 10-9)/(2.857 X 10-6)     = 38.20o

The difference is 5.34o so this, 3500 lines/cm, is the coursest grating you can use.

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