SSM A diffraction grating has resolving power R = λ avg /Δ λ = Nm. (a) Show that the corresponding frequency range ∆ƒ that can just be resolved is given by ∆ƒ = c/Nmλ. (b) From Fig. 36-22, show that the times required for light to travel along the ray at the bottom of the figure and the ray at the top differ by ∆ t = ( Nd/c ) sin θ. (c) Show that (∆ƒ)(∆ t ) = 1, this relation being independent of the various grating parameters. Assume N ≫1.
SSM A diffraction grating has resolving power R = λ avg /Δ λ = Nm. (a) Show that the corresponding frequency range ∆ƒ that can just be resolved is given by ∆ƒ = c/Nmλ. (b) From Fig. 36-22, show that the times required for light to travel along the ray at the bottom of the figure and the ray at the top differ by ∆ t = ( Nd/c ) sin θ. (c) Show that (∆ƒ)(∆ t ) = 1, this relation being independent of the various grating parameters. Assume N ≫1.
SSM A diffraction grating has resolving power R= λavg/Δλ= Nm. (a) Show that the corresponding frequency range ∆ƒ that can just be resolved is given by ∆ƒ = c/Nmλ. (b) From Fig. 36-22, show that the times required for light to travel along the ray at the bottom of the figure and the ray at the top differ by ∆t = (Nd/c) sin θ. (c) Show that (∆ƒ)(∆t) = 1, this relation being independent of the various grating parameters. Assume N ≫1.
..40 Go Figure 36-45 gives the pa- ß (rad)
rameter of Eq. 36-20 versus the ßs
sine of the angle in a two-slit inter-
ference experiment using light of
wavelength 435 nm. The vertical axis
scale is set by B, = 80.0 rad. What are
(a) the slit separation, (b) the total
number of interference maxima
(count them on both sides of the
pattern's center), (c) the smallest angle for a maxima, and (d) the
greatest angle for a minimum? Assume that none of the interference
maxima are completely eliminated by a diffraction minimum.
0
sin 0
0.5
1
Figure 36-45 Problem 40.
Light of free-space wavelength 20 = 0.75 um is guided by a thin planar film of thickness d=2.5 μm and refractive index ni = 1.65, surrounded by a medium of refractive index n2 =1.45.
(a) Determine
(i) the critical angle Oc;
(ii) the numerical aperture NA; and
(iii) the maximum acceptance angle ao for light originating in air (no = 1.00).
(b) Determine the number of TE modes possible at this wavelength. Determine
(i) the propagation angle a and
(ii) the propagation constant ß of the m= 0 TE mode (you will need to find a graphical or numerical approximate solution here). (iii) What is the wavelength of this mode inside the medium, measured along the z axis?
(d)
(i) Determine the extinction coefficient y for the same m= O mode.
(ii) At what distance into the outer medium does the field drop to 1% of its magnitude at the boundary?
www In Fig. 35-48,
an airtight chamber of length d
5.0 cm is placed in one of the arms
of a Michelson interferometer. (The
glass window on each end of the cham-
ber has negligible thickness.) Light of
wavelength A = 500 nm is used.
Evacuating the air from the chamber
causes a shift of 60 bright fringes. From
these data and to six significant figures,
81 SSM
Mirror
%3D
Source
Mirror
To vacuum
find the index of refraction of air at
pump
atmospheric pressure.
Chapter 36 Solutions
Fundamentals of Physics Extended - eText Regulation Card
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