15.2 Problems
721
tinctness of D 1 and D 2 lines of sodium is 2.89 × 10 −5 cm. Calculate λ
assuming that λ 1 ≈ λ 2 = 5.89 × 10 −5 cm.
15.39 In Michelson’s interferometer 100 fringes cross the field of view when the
movable mirror is displaced through 0.02948 mm. Calculate the wavelength
of the monochromatic light used.
[Delhi University]
15.40 The plates of Fabry – Perot interferometer have a reflectance amplitude of
r = 0.90. Calculate the resolving power of wavelengths near 600 nm when
the plates are separated by 2 mm.
[University of Wales, Aberystwyth 2005]
15.2.5 Diffraction
15.41 In Fraunhofer diffraction due to a narrow slit a screen is placed 2 m away
from the lens to obtain the pattern. If the slit width is 0.2 mm and the first
minima are 5 mm on either side of the central maximum, find the wavelength
of light.
[Delhi University]
15.42 The intensity I θ for the single-slit diffraction pattern is given by I θ = I m
(sin α/α) 2 , where α =
πa
λ
sin θ , and I m is the intensity of the central maximum. Show that the intensity maxima can be found out from the condition,
tan α = α.
15.43 (a) Obtain the expression for θ, the half-width at half central maximum of
single-slit Fraunhofer diffraction.
(b) Calculate θ for
a
λ
= 4.
[Osmania University]
15.44 A beam of light contains a mixture of wavelengths λ 1 and λ 2 . When the light
is incident on a single slit the first diffraction minimum of λ 1 coincides with
the second minimum of λ 2 . How are the two wavelengths related?
15.45 A single slit is illuminated normally by a monochromatic light of wavelength
of 5600 Å and diffraction bands are observed on a screen 2 m away. If the
centre of the second dark band is 1.6 cm from the central bright band, deduce
the slit width.
15.46 (a) What are missing orders in the double-slit diffraction pattern? Explain.
(b) Deduce the missing order for a double-slit diffraction pattern, if the slit
widths are 0.16 mm and they are 0.8 mm apart.
[Brahampur University]
721
tinctness of D 1 and D 2 lines of sodium is 2.89 × 10 −5 cm. Calculate λ
assuming that λ 1 ≈ λ 2 = 5.89 × 10 −5 cm.
15.39 In Michelson’s interferometer 100 fringes cross the field of view when the
movable mirror is displaced through 0.02948 mm. Calculate the wavelength
of the monochromatic light used.
[Delhi University]
15.40 The plates of Fabry – Perot interferometer have a reflectance amplitude of
r = 0.90. Calculate the resolving power of wavelengths near 600 nm when
the plates are separated by 2 mm.
[University of Wales, Aberystwyth 2005]
15.2.5 Diffraction
15.41 In Fraunhofer diffraction due to a narrow slit a screen is placed 2 m away
from the lens to obtain the pattern. If the slit width is 0.2 mm and the first
minima are 5 mm on either side of the central maximum, find the wavelength
of light.
[Delhi University]
15.42 The intensity I θ for the single-slit diffraction pattern is given by I θ = I m
(sin α/α) 2 , where α =
πa
λ
sin θ , and I m is the intensity of the central maximum. Show that the intensity maxima can be found out from the condition,
tan α = α.
15.43 (a) Obtain the expression for θ, the half-width at half central maximum of
single-slit Fraunhofer diffraction.
(b) Calculate θ for
a
λ
= 4.
[Osmania University]
15.44 A beam of light contains a mixture of wavelengths λ 1 and λ 2 . When the light
is incident on a single slit the first diffraction minimum of λ 1 coincides with
the second minimum of λ 2 . How are the two wavelengths related?
15.45 A single slit is illuminated normally by a monochromatic light of wavelength
of 5600 Å and diffraction bands are observed on a screen 2 m away. If the
centre of the second dark band is 1.6 cm from the central bright band, deduce
the slit width.
15.46 (a) What are missing orders in the double-slit diffraction pattern? Explain.
(b) Deduce the missing order for a double-slit diffraction pattern, if the slit
widths are 0.16 mm and they are 0.8 mm apart.
[Brahampur University]