748
15 Optics
Fig. 15.33 b Newton’s rings
formed by two curved
surfaces with centres of
curvature on the opposite side
AC = BC + AB
t =
r 2
m
2
1
R 1
+
1
R 2
(7)
2t = mλ
(dark fringes)
(8)
Eliminating t between (7) and (8)
r
2
m
1
R 1
+
1
R 2
= mλ
(m = 0, 1, 2 . . . , dark fringes)
(9)
2t =
m +
1
2
λ
(bright fringes)
(10)
Eliminating t between (7) and (10)
r
2
m
1
R 1
+
1
R 2
=
m +
1
2
λ
(m = 0, 1, 2 . . . , bright fringes)
(11)
15.31 x m =
m λ 1 D
d
= (m + 1)λ 2
D
d
m × 780 = (m + 1) × 520
∴ m = 2
15.32 Let the amplitude of the incident beam be a and intensity I :
I = a
2
The intensity of the reflected beam from the first face, Fig. 15.13
I 1 =
1
4
I
(by problem)
∴ a 1 =
a
2
15 Optics
Fig. 15.33 b Newton’s rings
formed by two curved
surfaces with centres of
curvature on the opposite side
AC = BC + AB
t =
r 2
m
2
1
R 1
+
1
R 2
(7)
2t = mλ
(dark fringes)
(8)
Eliminating t between (7) and (8)
r
2
m
1
R 1
+
1
R 2
= mλ
(m = 0, 1, 2 . . . , dark fringes)
(9)
2t =
m +
1
2
λ
(bright fringes)
(10)
Eliminating t between (7) and (10)
r
2
m
1
R 1
+
1
R 2
=
m +
1
2
λ
(m = 0, 1, 2 . . . , bright fringes)
(11)
15.31 x m =
m λ 1 D
d
= (m + 1)λ 2
D
d
m × 780 = (m + 1) × 520
∴ m = 2
15.32 Let the amplitude of the incident beam be a and intensity I :
I = a
2
The intensity of the reflected beam from the first face, Fig. 15.13
I 1 =
1
4
I
(by problem)
∴ a 1 =
a
2