# Diffraction grating

A diffraction grating consists of many narrow, parallel slits equally spaced.

A parallel bundle of rays falls perpendicular  to the grating

In each slit the light bends in every direction.

Behind the grating is interference .

In certain directions the waves interfere constructively.

This is at a path difference of rays from successive slits  of  0 λ , 1λ , 2 λ , etc

Diffraction grating equation:

n λ =  d sin αn

• λ   wavelength
• d   grating constant (distance between the slits)
• αn  angle of the maxima
• n   order maximum   1, 2, 3 …

For  the first order           :  λ  = d sin α1

For  the second order      : 2λ = d sin α2

Example

Perpendicular to a grating falls a parallel bundle of rays.

The grating has 5,000 slits per cm. At a distance of 2.00 m is a screen parallel at the grating.  The distance between the both 2e order maxima is 3.20 m.

Calculate the wavelength of the light.

d = 1/5000 = 2.00 x 10-4 cm = 2.00 x 10-6 m

x2= 1.60 m       tan α2=1.60/2.00 = 0.800

α2= 38.660 o

sin α2=0.625

2 λ = d sin α2     2 λ =( 2.00 x 10-6) 0.625       λ= 6.3 x 10-7 m 