# Diffraction Grating Formula

A diffraction grating defines an optical component with a periodic structure that splits the light into various beams that travel in different directions. It is an alternative way to observe spectra other than a prism. Generally, when light is incident on the grating, the split light will have maxima at an angle θ.  The formula for diffraction grating is used to calculate the angle.

## Diffraction grating formula

$\lambda n =dSin \theta _{n}$

Where,

• n is the order of grating,
• d is the distance between two fringes or spectra
• λ is the wavelength of light
• θ is the angle to maxima

### Solved Examples

Question 1: A diffraction grating is of width 5 cm and produces a deviation of  30in the second-order with the light of wavelength 580 nm. Find the slit spacing.

Solution:

Given: Angle θ =300, order n = 2, wavelength λ = 580 nm.

The slit spacing is given by,

$\lambda n =dSin \theta _{n}$

d = 2×580×10-9 /sin $30^{0}$

$d=2.320\times10^{-6}$ m