756
15 Optics
15.55 In Fig. 15.34 the grating space AD = d. In the ABD, B ˆ
AD = i, the angle
of incidence. Also D ˆ
AC = θ , the angle of diffraction. In the ABD, BD the
path difference between the incident rays, YD and XA is
BD = d sin i
Fig. 15.34 Diffraction by a
grating for a parallel beam of
light which is obliquely
incident
Similarly, the path difference between the diffracted rays is
DC = d sin θ
The total path difference
BD + DC = d(sin i + sin θ)
(1)
For the mth primary maximum
d(sin θ m + sin i) = mλ
(2)
or
sin
θ m + i
2
=
mλ
2d cos
θ m − i
2
(3)
The angle of deviation of the diffracted beam is
δ m = θ m + i
(4)
For δ m to be minimum, cos
θ m − i
2
must be maximum, that is
(θ m − i)/2 = 0 → θ m = i
(5)