As shown in Fig.2.1 and Fig.2.2,*α* is the angle between the incident light and the normal to the grating **(the incident angle)** and *ß* is the angle between the diffracted light and the normal to the grating **(the diffraction angle)**, then, they satisfy the following relationship:

as shown in Fig.2.1, in case of transmission grating

as shown in Fig.2.2 in case of a reflection grating,

*d* : Spacing between the slits **(the grating period)**

*N* : Number of slits per mm (**the groove density**, equal to the reciprocal of the grating period)

*m* : **Order of diffraction** (*m* = 0, ± 1, ± 2,...)

λ : Wavelength

It can be seen from this relationship that all components of light corresponding to *m* = 0 **(zero-order light)** are radiated in a straight line and so it is not possible to separate the wavelengths with this order. It can also be seen that for *m* ≠ 0 the diffraction angle *ß* is different for each wavelength. This is why gratings can be used to separate white light into its constituent wavelengths. The diffraction angle *ß* also varies with the groove density *N* and the incident angle *α*. One point requiring consideration is that, depending on the groove density *N*, it may not be possible to obtain diffracted light. For example, if the incident angle *α* = 30° and the groove density *N* = 2400 grooves/mm, applying the equation to **first-order light** (i.e., *m* = +1) with a wavelength λ of 700nm gives sin *ß* = 1.18, then diffracted light cannot be obtained in this case.

- SHIMADZU DIFFRACTION GRATINGS
- 01. Introduction to Diffraction Gratings
- 02. What are Diffraction Gratings
**03. The Grating Equations**- 04. Dispersion
- 05. Grating Resolution
- 06. Free Spectral Range
- 07. Blaze Wavelength
- 08. Diffraction Efficiency & Relationship between Diffraction Efficiency and Polarization
- 09. Anomalies
- 10. Profile of Grating Grooves
- 11. Toroidal Diffraction Gratings
- 12. Replicas
- 13. Coatings
- 14. Transmission Gratings
- 15. Choice of a Grating
- 16. Handling of Gratings