15.3 Solutions
757
Then δ m will be minimum, say D m , and is given by
D m = θ m + i = 2i
or
i = D m /2
( 6 )
Substituting (5) and (6) into (3)
2d sin
D m
2
= mλ
(7)
N =
1
d
=
2 sin(20/2)
1 × 4.358 × 10 −5 = 7969 lines/cm
15.56 Condition for overlapping is
mλ 1 = (m + 1)λ 2
5400 m = 4050 × (m + 1)
∴ m = 3
d sin θ = mλ 1
N =
1
d
=
sin θ
mλ 1
=
sin 30 ◦
3 × 5.4 × 10 −5
= 3086 lines/cm
15.57 λ = 5893 Å = 5.893 × 10 −5 cm
λ = λ 1 − λ 2 = 5896 − 5890 = 6 Å = 6 × 10
−8 cm
Resolving power
R =
λ
dλ
=
5.893 × 10 −5
6 × 10 −8 = 982
R = N m
∴ N =
R
m
=
982
2
= 491
(Total number of lines)
If N is the number of lines/cm, then the width of the grating
W =
N
N =
491
800
= 0.614 cm
15.58 Total number of lines on the grating
N = N
W
(1)
757
Then δ m will be minimum, say D m , and is given by
D m = θ m + i = 2i
or
i = D m /2
( 6 )
Substituting (5) and (6) into (3)
2d sin
D m
2
= mλ
(7)
N =
1
d
=
2 sin(20/2)
1 × 4.358 × 10 −5 = 7969 lines/cm
15.56 Condition for overlapping is
mλ 1 = (m + 1)λ 2
5400 m = 4050 × (m + 1)
∴ m = 3
d sin θ = mλ 1
N =
1
d
=
sin θ
mλ 1
=
sin 30 ◦
3 × 5.4 × 10 −5
= 3086 lines/cm
15.57 λ = 5893 Å = 5.893 × 10 −5 cm
λ = λ 1 − λ 2 = 5896 − 5890 = 6 Å = 6 × 10
−8 cm
Resolving power
R =
λ
dλ
=
5.893 × 10 −5
6 × 10 −8 = 982
R = N m
∴ N =
R
m
=
982
2
= 491
(Total number of lines)
If N is the number of lines/cm, then the width of the grating
W =
N
N =
491
800
= 0.614 cm
15.58 Total number of lines on the grating
N = N
W
(1)