718
15 Optics
Fig. 15.10
15.21 A beam of monochromatic light with wavelength λ is incident upon two slits
S 1 and S 2 a distance d apart, as shown in Fig. 15.11. Derive an expression,
in terms of λ, L, d, and m for the distance y m from the central point to the
mth bright fringe of the interference pattern on a screen a distance L away
when L >> y m .
Two narrow slits separated by 2 mm are illuminated with a helium–neon
laser of wavelength 612 nm. Calculate the spacing of the fringes observed on
a screen 4 m.
Fig. 15.11
15.22 When a thin transparent plate of thickness t and refractive index μ is introduced in the path of one of the two interfering monochromatic beams of
wavelength λ in Young’s double-slit experiment, then fringes are shifted.
Show that (μ − 1)t = nλ.
15.23 In Young’s double-slit experiment the bandwidth β is given by the expression: β =
λL
d
, where L is the slit-screen distance, d is the slit separation and
λ is the wavelength of light used:
(a) Obtain an expression for the intensity distribution in the fringe system
of Young’s double-slit experiment.
(b) Hence show that the average intensity of the fringes is equal to 2I , where
I is the intensity of each beam.
15.24 In a Fresnel’s biprism experiment, the bandwidth of 0.195 mm is observed
at a distance of 1 m from the slit. The image of the coherent sources is then
produced at the same distance from the slit by placing a convex lens a 30 cm
from the slit. Two images are found to be separated by 0.7 cm. Calculate the
wavelength of light used.
[Kakatiya University 2002]
15 Optics
Fig. 15.10
15.21 A beam of monochromatic light with wavelength λ is incident upon two slits
S 1 and S 2 a distance d apart, as shown in Fig. 15.11. Derive an expression,
in terms of λ, L, d, and m for the distance y m from the central point to the
mth bright fringe of the interference pattern on a screen a distance L away
when L >> y m .
Two narrow slits separated by 2 mm are illuminated with a helium–neon
laser of wavelength 612 nm. Calculate the spacing of the fringes observed on
a screen 4 m.
Fig. 15.11
15.22 When a thin transparent plate of thickness t and refractive index μ is introduced in the path of one of the two interfering monochromatic beams of
wavelength λ in Young’s double-slit experiment, then fringes are shifted.
Show that (μ − 1)t = nλ.
15.23 In Young’s double-slit experiment the bandwidth β is given by the expression: β =
λL
d
, where L is the slit-screen distance, d is the slit separation and
λ is the wavelength of light used:
(a) Obtain an expression for the intensity distribution in the fringe system
of Young’s double-slit experiment.
(b) Hence show that the average intensity of the fringes is equal to 2I , where
I is the intensity of each beam.
15.24 In a Fresnel’s biprism experiment, the bandwidth of 0.195 mm is observed
at a distance of 1 m from the slit. The image of the coherent sources is then
produced at the same distance from the slit by placing a convex lens a 30 cm
from the slit. Two images are found to be separated by 0.7 cm. Calculate the
wavelength of light used.
[Kakatiya University 2002]