Homework Assignment 11
Physics 142, General Physics II
Spring 2017
Problems
Problem 1
(a) Light of wavelength 633 nm falls on a slit 0.040 mm wide.
(1) On a very large and distant screen, how many totally dark fringes (indicating complete cancellation) will there be, including both sides of the central bright spot? Solve this problem without
calculating all the angles!
(2) Find the angles for the dark fringes which are most distant from the central bright fringe.
(b) Monochromatic light from a distant source is incident on a slit 0.60 mm wide. On a screen 1.5 m away,
the distance from the central maximum of the diffraction pattern to the first minimum is measured
to be 1.2 mm. Calculate the wavelength of the light.
Problem 2
(a) Consider the interference pattern produced by two parallel slits of width a and separation d, in which
d = 3a. The slits are illuminated by normally incident light of wavelength λ.
(1) First we ignore diffraction effects due to the slit width. At what angles θ from the central
maximum will the next four maxima in the two-slit interference pattern occur? Your answer will
be in terms of d and λ.
(2) Now we include the effects of diffraction. If the intensity at θ = 0 is I0 , what is the intensity at
each of the angles in part (a)?
(3) Which double-slit interference maxima are missing in the pattern?
(b) A diffraction experiment involving two thin parallel slits yields the pattern of closely spaced bright
and dark fringes shown in the figure. Only the central portion of the pattern is shown in the figure.
The bright spots are equally spaced at 1.53 mm center to center (except for the missing spots) on a
screen 3.0 m from the slits. The light source was a He-Ne laser producing a wavelength of 632.8 nm.
(1) How far apart are the two slits?
(2) How wide is each one?
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Problem 3
A few questions about optical resolving power using the Rayleigh criterion.
(a) The resolution of an optical microscope can be increased by immersing the objective lens and the
sample in a transparent oil. Why does this work?
(b) Radio telescopes make images of distant objects using the waves emitted in the radio part of the
spectrum. If a radio telescope receiving waves with λ = 3 cm is to have the same resolution the 5 m
(diameter) Hale telescope has with 500 nm light, how large must the diameter of the antenna be?
(c) Callisto is the Galilean moon with the largest orbit, a maximum distance of about 2 × 106 kilometers
from Jupiter. At its closest point to the earth, it is about 6 × 108 kilometers away. Is it possible for
a human with a normal eye to make out this Galilean moon on a really clear night?
[In your estimate, you can pick any wavelength in the visible range, say 600 nm. In darkness, a dilated
pupil can be as large as 8 mm in diameter. The angular resolution of a normal human eye limited by
the size of the retinal cells is about 1 arc minute.]
Problem 4
Two problems about diffraction gratings.
(a) The wavelength range of the visible spectrum is approximately 380–750 nm. White light falls at
normal incidence on a diffraction grating that has 400 slits/mm.
(1) Find the angular width of the visible spectrum in the first order.
(2) Find the angular width of the visible spectrum in the third order.
(3) What is the longest wavelength that can be observed in the third order for this grating?
(b) When laser light of wavelength 632.8 nm passes through a diffraction grating, the first bright spots
occur at ±18.0◦ from the central maximum.
(1) What is the line density (in lines cm) of this grating?
(2) How many additional bright spots are there beyond the first bright spots, and at what angles
do they occur?
Problem 5
Different isotopes of the same element emit light at slightly different wavelengths. A wavelength in the
emission spectrum of a hydrogen atom is 656.45 nm; for deuterium, the corresponding wavelength is 656.27
nm.
(a) What minimum number of slits is required to resolve these two wavelengths in second order?
(b) If the grating has 500.0 slits/mm, find the angles and angular separation of these two wavelengths in
the second order.
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