A diffraction grating with 750 slits per mm is illuminated by light which gives a first-order diffraction angle of 34.0 degrees.

What is the wavelength of the light?

please help, im pretty desperate

### 2 Answers

the diffraction formula is Dsin(theta) = lambda

1. the problem tells us the diffraction grating is 750 slits per mm so that will be (1/750mm); however the answer asks for the units in nanometers so I converted that first

1/750mm * (1,000,000 nm/1mm) = 1.33 x 10^3 nm

– from there, multiple (sin34) x (1.33 x 10^3nm) = 746 nm