Violet light (wavelength = 414 nm) and red light (wavelength = 672 nm) lie at op

Question

Violet light (wavelength = 414 nm) and red light (wavelength = 672 nm) lie at opposite ends of the visible spectrum. For each wavelength, find the angle that locates the first-order maximum produced by a grating with 3370 lines/cm. This grating converts a mixture of all colors between violet and red into a rainbow-like dispersion between the two angles [(a) will be the angle for the violet light, and (b) will be the angle for the red light)]. Repeat the calculation above for the second-order maximum [(c) (violet), (d) (red)] and the third-order maximum [(e) (violet), (f) (red)]. Finally, (g) from your results, decide whether there is an overlap between any of the "rainbows" and, if so, specify which orders overlap.

Explanation / Answer

d sin theta = n lambda for a maximum and d = 1/N (lines per m)

so sintheta = n lambda/d = n N lambda with n=1 first order n =2 second order etc

a) sintheta = 1 x 3.455 x 10^5 x 438 x 10^-9 giving theta = 8.704 degrees

repeat for the other cases and see if any overlap

b) 13.10 deg
c) 17.61 deg
d) 26.96 deg
e) 27.00 deg
f) 42.84 deg

so d) and f) overlap = 2nd and 3rd.

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