PROBLEM SET #5

DIFFRACTION

A01. Diffraction of sound waves is more readily observable than that of light waves because
A) sound waves are longitudinal and not transverse.
B) sound waves have a higher frequency than light waves.
C) sound waves have a lower velocity than light waves.
D) sound waves have longer wavelengths than do light waves.
E) interference occurs more readily for longitudinal waves.

A02. When a parallel beam of light is diffracted at a single slit,

A) the shadow is always sharp.
B) the narrower the slit, the narrower the central diffraction maximum.
C) the narrower the slit, the wider the central diffraction maximum.
D) the width of the central diffraction maximum is independent of the width of the slit.
E) None of these is correct.

A03. The graphs are plots of relative intensities of various diffraction patterns versus the sine
of the angle from the central maximum. The graph that represents the diffraction pattern
from the widest single slit is
A) 1
B) 2
C) 3
D) 4
E) 5

A04. The diffraction pattern of a single slit is shown in the figure. The point at which the path
difference of the extreme rays is two wavelengths is
A) 1
B) 2
C) 3
D) 4
E) 5

A05. In dealing with the diffraction pattern of a single slit, we are usually interested in the
location of the first minimum in light intensity because
A) it is the only one that can be determined accurately.
B) it is the only one for which the small-angle approximation holds.
C) nearly all the light energy is contained in the central maximum.
D) it is the only one for which the location is directly proportional to the wavelength of
the light.
E) it is the only one that can be described by Fraunhofer diffraction.

Solutions available at http://departments.johnabbott.qc.ca/departments/physics/?target=solutions

 Problem Set 5

A06. As the width of the slit producing a single-slit diffraction pattern is slowly and steadily
reduced (always remaining larger than the wavelength of the light), the diffraction pattern
A) slowly and steadily gets wider.
B) slowly and steadily gets brighter.
C) does not change because the wavelength of the light does not change.
D) slowly and steadily gets narrower.
E) None of these is correct.

A07. Which of the phasor diagrams

shows the first minimum for
five equally spaced in-phase
sources?
A) 1
B) 2
C) 3
D) 4
E) 5

A08. Which of the following statements concerning the

interference pattern described by the phasor diagram is true?
A) There are exactly seven coherent sources.
B) There is a relative minimum at the point in the pattern
corresponding to the phasor diagram.
C) The amplitude of the resultant wave at the point in the
pattern corresponding to the phasor diagram is less than
the sum of the amplitudes of the individual waves.
D) The diagram corresponds to the third bright spot in the interference pattern.
E) None of these is correct.

A09. A student looks through a transmission grating at the light from a helium light source. He
sees the red, yellow, and green light from the source superimposed on a meterstick. If the
yellow lines are the ones indicated in the figure, then

A) 1 and 2 are green; 3 and 4 are red.

B) 1 and 4 are red; 2 and 3 are green.
C) 1 and 4 are green; 2 and 3 are red.
D) 1 and 3 are red; 2 and 4 are green.
E) 1 and 3 are green; 2 and 4 are red.

Solutions available at http://departments.johnabbott.qc.ca/departments/physics/?target=solutions

 Problem Set 5

A10. In the following experiments, two equally bright point sources of monochromatic light are
brought together until they can barely be resolved by an observer. In which case are they
brought closest together?
A) The sources are blue, and they are observed under dark conditions so that the pupil of
the eye is maximally dilated.
B) The sources are blue, and they are observed under bright conditions so that the pupil
of the eye is minimally dilated.
C) The sources are red, and they are observed under dark conditions.
D) The sources are red, and they are observed under bright conditions.
E) Both B) and D) are correct.

A11. Although we can hear around corners, we cannot see around corners. How can you explain
this in view of the fact that both light and sound are waves?

A12. A loudspeaker horn used at a rock concert has dimensions 100 cm by 30 cm. Should it be
oriented with the long axis vertical or horizontal? Why?

A13. Why is it that diffraction gratings are made with so many lines so close together?

B01. Light with a wavelength of 550 nm is shone through a slit onto a screen 2.50 m away. If the
width of the central maximum is 7.0 mm, what is the width of the slit?

B02. Light with a wavelength of 630 nm is incident upon a slit which is 0.15 mm wide. A
diffraction pattern is observed on a screen 3.00 m from the slit.
a) What is the distance on the screen from the middle of the central maximum to the first
minimum?
b) What is the intensity at a point halfway between the center of the pattern and the first
minimum, as a percent of the intensity at the center?

B03. The fringe pattern shown below is observed on a screen that is 4.00 m from a double slit.
If light with wavelength 546 nm is illuminating the double slit,
a) What is the separation of the slits?
b) What is the width of each slit?

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 Problem Set 5

B04. Two identical slits of unknown width and unknown spacing are illuminated by laser light
of λ = 630 nm. One of the slits is covered and a single slit diffraction pattern is observed
on a screen 4.00 m away. The distance from the central maximum to the first minimum is
measured to be 3.15 cm. The second slit is now uncovered and the spacing between
successive maxima in the double slit pattern is measured to be 1.05 cm.
a) What is the width of each slit?
b) What is the center to center spacing between the slits?
c) What will be the first missing order in the double slit pattern?
d) How many fringes are there in the principal maximum of the fringe envelope?
e) Sketch the graph of intensity vs position measured along the screen. Show the first
and second missing orders on your sketch.

B05. Monochromatic coherent light of λ = 500 nm is being used in a four-slit interference

experiment. The distance between the slits is 0.03 mm and the slit width is 0.01 mm.
a) Find the interference phase angle of the first interference principal maximum.
b) Find the interference phase angle of all the minima between the central maximum and
the first interference principal maximum.
c) Find the intensity of the third principal interference maximum relative to the intensity
of the central maximum.
d) Find the intensity of the central maximum relative to the intensity of light passing
through each slit.

B06. White light falls at normal incidence on a diffraction grating with 350 lines per mm. Find
the angular width of the visible spectrum
a) in the first order
b) in the third order.

B07. The tracks of the tiny pits in which information is coded on a compact disk are 1.60 µm
apart. If laser light with a wavelength of 632.8 nm is shone perpendicular to this CD, at
what angles of reflection will the intensity of the light be maximum?

B08. What is the minimum distance between two points of light that will still allow them to be
resolved at a distance of 1 km
a) with the unaided eye (ignore the fact that the index of refraction of the eye is not 1).
[What assumptions do you have to make?!]
b) using a telescope with an aperture of 10 cm?
c) How would your answer to a) change if you took into account the fact that the index
of refraction of the eye is not 1?

Solutions available at http://departments.johnabbott.qc.ca/departments/physics/?target=solutions