15.1 Basic Concepts and Formulae
709
Relative intensities of the secondary maxima
I θ = I max
sin α
α
2
(15.31)
where α =
πa
λ
sin θ
(15.32)
I θ
I max
=
⎛
⎜
⎜
⎝
sin
m +
1
2
π
m +
1
2
π
⎞
⎟
⎟
⎠
2
(15.33)
The secondary maxima lie approximately halfway between the minima.
Double-Slit and N-Slits (Grating)
I = I max
sin α
α
2 sin
2 Nβ
sin
2
β
(15.34)
where α =
πa sin θ
λ
and
β =
π d sin θ
λ
a is the slit width and d is the slit spacing. In (15.32) the first factor arises due to
diffraction from a single slit, the second one is due to interference of light waves
from different slits.
For N = 1 we obtain the single-slit pattern and for large N we are dealing with
a grating.
Maximum number of order
m max = a/λ
(15.35)
Condition for overlapping of spectral lines:
m 1 λ 1 = m 2 λ 2 = m 3 λ 3 = . . .
(15.36)
Missing orders: The missing orders occur when the condition for a maximum of
the interference and for a minimum of the diffraction are both fulfilled for the same
value of θ :
d sin θ = mλ, m = 0, 1, 2 . . .
a sin θ = pλ, p = 1, 2, 3, . . .
d
a
=
m
p
(15.37)