# Calculating wavelength of a 2D grating (different distances between slits)

#### Femke

For my report I need a formula to calculate the wavelength with a multiple slit experiment. I have found: d sin(\theta) = m \lambda.
However, for the experiment a two dimensional grating is used. The distance between the vertical slits are not the same as the distance between the horizontal slits. What formula can I use to calculate the wavelength?

I added an example to hopefully make it more clear. #### Woody

The asymmetric grating should not matter,
it will just give you an asymmetric interference pattern.
Note that rather than parallel lines of constructive and destructive interference
you will get a grid of constructive and destructive interference.
the (different) horizontal and vertical spacing of the interference will mirror the (different) horizontal and vertical spacing of the grid
and (of course) the wavelength (frequency) of the light.
Note that you actually get two equations from a single grid.

so you get:
$$\displaystyle d_{H} sin(\theta_{Hm}) = m \lambda$$
and:
$$\displaystyle d_{V} sin(\theta_{Vm}) = m \lambda$$
Where the V and H subscripts indicate the vertical and horizontal grids respectively.

• donglebox