No idea how to get started and proffessor did not lecture on this amterial befor

Question

No idea how to get started and proffessor did not lecture on this amterial before assingning. I have looked in the book and cannot figure it out. Would like all, but an example for one of each would probably help me get there.

A diffraction grating is used to seperate different wavelengths of white light. Three discrete first-order spectral lines occur at angles of 10.1 13.61, 14.75. If the grating has 3667 slits/cm, what are the wavelengths of the light? nm nm nm At what angles are these lines found in the second-order spectrum degrees degrees degrees

Explanation / Answer

N = 3667 slits/cm = 366700 slits/m

N = 1/d

dsin(theta) = n*lamda

sin(theta) = 1*lamda*N

for theta = 10.1 degrees

sin(10.1) =1*lamda*366700

lamda = 478 nm

for theta = 13.61 degrees

sin(13.61) =1*lamda*366700

lamda = 642 nm

for theta = 14.75 degrees

sin(14.75) =1*lamda*366700

lamda = 694 nm

for n = 2

dsin(theta) = n*lamda

theta = arcsin(2*lamda*366700)

for lamda = 478 nm

theta = arcsin(2*478*10^-9*366700)

theta = 20.5 degrees

for lamda = 642 nm

theta = arcsin(2*642*10^-9*366700)

theta = 28.1 degrees

for lamda = 694 nm

theta = arcsin(2*694*10^-9*366700)

theta = 30.6 degrees

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