15.2 Problems
723
15.58 A grating of width 3 is ruled with 10,000 lines/in. Find the smallest wavelength separation that can be resolved in the first-order spectrum at a mean
wavelength of 6000 Å.
[Kakatiya University2002]
15.59 Examine two spectral lines of wavelengths 5890 and 5896 Å which can be
clearly resolved in the (i) first order and (ii) second order by diffraction grating 2 cm wide and having 425 lines/cm.
[Delhi University]
15.60 The refractive indices of a glass prism for the C and F lines are 1.6545 and
1.6635, respectively. The wavelength of these two lines in the solar spectrum
are 6563 and 5270 Å, respectively. Calculate the length of the base of 60 ◦
prism which is capable of resolving sodium lines of wavelengths 5890 and
5896 Å.
[Vikram University]
15.61 Find the separation of two points on the moon that can be resolved by a
500 cm telescope. The distance of the moon is 3.8 × 10 5 km from the earth.
The eye is most sensitive to light of wavelength 5500 Å.
[Nagpur University]
15.62 Lycopodium particles that have an average diameter of 30 μm are dusted on a
glass plate. If a parallel beam of light of wavelength 589 nm is passed through
the plate, what is the angular radius of the first diffraction maximum?
[Kakatiya University 2004]
15.63 The intensity distribution for Fraunhofer diffraction of a circular spectrum of
radius R is of the form
I = I 0
2J 1 (ρ)
ρ
2
where ρ =
2πa
λ
sin θ and J 1 (x) is the Bessel function of the first kind. Show
that by Rayleigh’s criterion the minimum angular resolution of a telescope is
given by θ ≈ 1.22
λ
D
, where D is the diameter of the circular aperture.
15.64 Calculate the radii of the 1st and 25th circles on a zone plate behaving like a
convex lens of focal length 50 cm for λ = 5000 Å.
[Kakatiya University]
723
15.58 A grating of width 3 is ruled with 10,000 lines/in. Find the smallest wavelength separation that can be resolved in the first-order spectrum at a mean
wavelength of 6000 Å.
[Kakatiya University2002]
15.59 Examine two spectral lines of wavelengths 5890 and 5896 Å which can be
clearly resolved in the (i) first order and (ii) second order by diffraction grating 2 cm wide and having 425 lines/cm.
[Delhi University]
15.60 The refractive indices of a glass prism for the C and F lines are 1.6545 and
1.6635, respectively. The wavelength of these two lines in the solar spectrum
are 6563 and 5270 Å, respectively. Calculate the length of the base of 60 ◦
prism which is capable of resolving sodium lines of wavelengths 5890 and
5896 Å.
[Vikram University]
15.61 Find the separation of two points on the moon that can be resolved by a
500 cm telescope. The distance of the moon is 3.8 × 10 5 km from the earth.
The eye is most sensitive to light of wavelength 5500 Å.
[Nagpur University]
15.62 Lycopodium particles that have an average diameter of 30 μm are dusted on a
glass plate. If a parallel beam of light of wavelength 589 nm is passed through
the plate, what is the angular radius of the first diffraction maximum?
[Kakatiya University 2004]
15.63 The intensity distribution for Fraunhofer diffraction of a circular spectrum of
radius R is of the form
I = I 0
2J 1 (ρ)
ρ
2
where ρ =
2πa
λ
sin θ and J 1 (x) is the Bessel function of the first kind. Show
that by Rayleigh’s criterion the minimum angular resolution of a telescope is
given by θ ≈ 1.22
λ
D
, where D is the diameter of the circular aperture.
15.64 Calculate the radii of the 1st and 25th circles on a zone plate behaving like a
convex lens of focal length 50 cm for λ = 5000 Å.
[Kakatiya University]