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