758
15 Optics
where N = number of lines/in. and W is the grating width (in inch)
∴ N = 10, 000 × 3 = 30, 000
R =
λ
dλ
= N m
∴ dλ =
λ
N m
=
6 × 10 −5
3 × 10 4 × 1
= 2 × 10
−9 cm = 0.2 Å
15.59 Total number of lines
N = N
W = 2 × 425 = 850
λ = 5893 Å, dλ = 5896 − 5890 = 6 Å
(i) First order:
R =
λ
dλ
= N m
N =
1
m
λ
dλ
=
1
1
×
5893
6
= 982 lines
As the required number of lines (982) exceeds the total number of lines
(850) the lines are not resolved in the first order.
(ii) Second order
N =
1
m
λ
dλ
=
1
2
×
5893
6
= 491
As the required number of lines (491) is less than the total number of
lines, the lines are resolved in the second order.
15.60 The resolving power for a prism of base length B is given by
R =
λ
λ
=
Bdμ
dλ
(1)
where dμ/dλ is the variation of refraction index of the prism with wavelength, λ is the mean wavelength and λ is the difference in wavelengths to
be resolved:
λ = 5893 Å, ,λ = 5896 − 5890 = 6 Å
dμ
dλ
=
1.6635 − 1.6545
(6563 − 5270) × 10 −8 cm
= 696/ cm
Substituting the above values in (1) and solving for B, we find the length of
the base of the prism, B = 1.41cm.