3.3.2.2
Deriving the grating equation from path difference and trigonometry
Interference & Diffraction — AQA A-Level Physics
- At the zeroth order (n = 0), path differenceThe difference in distance travelled by two waves from their sources to a given point. Determines whether constructive or destructive interference occurs. between adjacent slits is zero.
- At the first order (n = 1), constructive interference requires a path differenceThe difference in distance travelled by two waves from their sources to a given point. Determines whether constructive or destructive interference occurs. of one wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m)..
- From the geometry of adjacent slits separated by distance d, the path differenceThe difference in distance travelled by two waves from their sources to a given point. Determines whether constructive or destructive interference occurs. is $d \sin \theta$.
- For the first order: $\sin \theta_1 = \lambda / d$.
- For the nth order: $\sin \theta_n = n\lambda / d$.
- Rearranging: $d \sin \theta = n\lambda$.