Principles of Technology
CH 13 LIGHT AND GEOMETRIC OPTICS
5
Name____
KEY OBJECTIVES
At the conclusion of this chapter you will be able to:
• Define the terms chromatic aberration and spherical aberration, and describe these defects.
• Describe the patterns produced when monochromatic light passes through a double-slit arrangement, and explain
how these patterns are formed.
• Apply the double-slit equation to the solution of problems.
• Explain the difference between the pattern produced by a double- slit arrangement and that produced by a singleslit arrangement.
• Define the term thin-film interference, and explain why soap bubbles and oil slicks produce colored patterns when
illuminated by white light.
• Define the term laser, and explain how laser light differs from ordinary light.
LENS DEFECTS
Two types of defects are common to all types of simple lenses. Chromatic aberration occurs because different
colors of light do not focus at the same point. In cameras, this type of lens defect can be reduced by using
combinations of lenses made of different types of glass.
Spherical aberration occurs because the spherical shape of the lens is not ideal for converging the light to a single
point. Spherical aberration may be reduced (in cameras, for example) by restricting the light beam close to the
center of the lens. This restriction is accomplished by reducing the size of the lens opening (the aperture).
1.
Which statement is false?
a. All types of defects that are common to all types of simple lenses can be repaired by reducing the size of
the lens opening (the aperture). This is done by increasing the aperture diameter.
b. Chromatic aberration occurs because different colors of light do not focus at the same point. In cameras,
this type of lens defect can be reduced by using combinations of lenses made of different types of glass.
c. Spherical aberration occurs because the spherical shape of the lens is not ideal for converging the light
to a single point.
d. Spherical aberration may be reduced (in cameras, for example) by restricting the light beam close to the
center of the lens.
13.7 DIFFRACTION AND INTERFERENCE OF LIGHT
The Double-Slit Experiment
If light is passed through a pair of closely spaced slits, an alternating pattern of bright and dark bands will appear on
a distant screen, as shown below.
To explain this phenomenon we must first consider how a wave can travel from one point to another. Danish
scientist Christian Huygens developed a principle that states that every point on a wave front can be considered a
point source of secondary spherical waves (called wavelets). After a time, the new location of the wave is found by
drawing a common tangent to these wavelets.
2.
Which statement is false?
a. If light is passed through a pair of closely spaced slits, an alternating pattern of bright and dark bands
will appear on a distant screen.
b. Every point on a wave front can be considered a point source of secondary spherical waves (called
wavelets).
c. After a time, the new location of the wave is found by drawing a common tangent to these wavelets.
d. Light is unaffected when it is passed through closely spaced slits.
In the double-slit arrangement illustrated below, each slit serves as a point source of waves. We see that, as the
waves grow, the wave fronts interfere with one another. Points that interfere constructively will ultimately pro duce
the bright bands, while points that interfere destructively will produce the dark bands, as shown in the diagram
below.
Wave fronts interference
Double-slit arrangement
3.
Which statement is false?
a. In a double-slit arrangement, each slit serves as a point source of waves.
b. Waves only increase magnitude when they are passed through a double-slit arrangement.
c. As the waves passing through a double-slit arrangement grow, the wave fronts interfere with one
another.
d. Points that interfere constructively will ultimately produce the bright bands, points that interfere
destructively will produce the dark bands.
We note that the bright bands are nearly evenly spaced. For very closely spaced slits the distance between any two
bright bands (X) depends on the wavelength of light used (X), the distance between the slits (a), and the distance
between the slits and the screen (L). In the diagram above, the central bright band is known as the zero-order band,
and consequent bright bands on either side of the central band are referred to as the first-order band, the secondorder band, and so on. The numerical relationship among the various factors is expressed by the following equation:
X = λL/d
4. Calculate the distance between the first two bright bands (X) of monochromatic light is incident on a pair of
slits 8.50 x 10-2 meter (d) apart and a wavelength is 5.80 x 10-2 meter (λ). If the distance between the slits and
the screen is 0.010 meter (L).
X = λL/d
-4
a. 5.01 x 10 meter
b. 0.0660 m
c. 0.493 m
d. 1.01 m
5.
Which statement is false?
The bright bands are nearly evenly spaced in a double-slit arrangement.
For very closely spaced slits the distance between any two bright bands (X) depends on the wavelength of
light used (X), the distance between the slits (a), and the distance between the slits and the screen (L). The
central bright band is known as the zero-order band, and consequent bright bands on either side of the central
band are referred to as the first-order band, the second-order band, and so on.
c.
The bright bands are always randomly spaced in a double-slit arrangement
d.
The numerical relationship among the various factors of the bright bands spacing in a double-slit arrangement
is expressed by the following equation: X = λL/d
a.
b.
As the wavelength of light increases, the distance between the bright bands increases. Also, as the distance between
the slits and the screen increases, the distance between the bright bands increases. However, as the distance between
the slits increases, the distance between the bright bands decreases. This relationship can be used to measure the
wavelength of monochromatic light. In this case we rewrite the equation as follows:
λ = dX/L
6.
Which statement is false?
a. As the wavelength of light increases, the distance between the bright bands increases.
b. As the distance between the slits and the screen increases, the distance between the bright bands
increases. As the distance between the slits increases, the distance between the bright bands decreases.
c. The relationship between slit distance and bright band distance can be used to measure the wavelength
of monochromatic light.
d. The distance between bright bands remains constant even if slit distance or wavelength are changed.
PROBLEM
Monochromatic light is incident on a pair of slits 1.95 x 10-5 meter (d) apart. The distance between the first two
bright bands is 2.11 x 10-2 meter (X). If the distance between the slits and the screen is 0.600 meter (L),
(a) calculate the wavelength (λ) and (b) state the color of the light.
λ = dX/L
SOLUTION
7. Calculate the wavelength (λ) of monochromatic light is incident on a pair of slits 9.50 x 10-2 meter (d) apart.
The distance between the first two bright bands is 8.80 x 10-2 meter (X). If the distance between the slits and
the screen is 0.110 meter (L).
λ = dX/L
a. 5.30 x 10-4 meter
b. 0.0760 m
c. 0.801 m
d. 1.30 m
Single-Slit Diffraction
A single slit can also be used to produce a diffraction pattern. The width of the slit must have the same order of
magnitude as the wavelength of the light used. The pattern produced by single-slit diffraction is different from the
pattern obtained with double-slit diffraction in two respects: the central bright band is much wider than any of the
other bright bands, and the intensity of the central band is greater than the intensity of any of the other bright bands.
Single-Slit Diffraction
Thin-Film Interference
8.
Which statement is false?
a. A single slit can also be used to produce a diffraction pattern. The width of the slit must have the
same order of magnitude as the wavelength of the light used.
b. The pattern produced by single-slit diffraction is the same as the pattern obtained with double-slit
diffraction in every way.
c. The central bright band is much wider than any of the other bright bands in single-slit diffraction.
d. The intensity of the central band is greater than the intensity of any of the other bright bands in
single-slit diffraction.
Thin-Film Interference
If a person observes an oil slick or a soap bubble that is illuminated with white light, he or she will see a series of
colors on the surface of the slick or bubble. This phenomenon, known as thin-film interference and diagramed
below, results when light waves reflected from the top of the film interfere with light waves reflected from the
bottom of the film.
The colors observed depend on the nature of the film (its refractive index) and the thickness of the film.
9.
Which statement is false?
a. If a person observes an oil slick or a soap bubble that is illuminated with white light, he or she
will see a series of colors on the surface of the slick or bubble.
b. Thin-film interference only results in one set of colors that occur in all situations regardless of
quantity and chemical composition.
c. The phenomenon known as thin-film interference, results when light waves reflected from the
top of the film interfere with light waves reflected from the bottom of the film.
d. The colors observed during thin-film interference depend on the nature of the film (its refractive
index) and the thickness of the film.
Lasers
When light (even monochromatic light) is emitted by a source, the light waves have no special (phase) relationship
with one another.
Incoherent Waves
Waves In Phase
As a result, the light beam spreads and loses its intensity (brightness) quickly. This light is said to be incoherent.
A laser is a device that produces monochromatic light in which nearly all of the waves are in phase.
The word laser is an acronym for light amplification by stimlated emission of radiation. The beam produced by a
laser spreads very little and is extraordinarily intense. This light is called coherent. Because of its properties, laser
light can be used for a variety of applications, from bar-code scanning to eye surgery.
The color of laser light depends on the sources that produce the light. Helium-neon lasers, for example, produce red
light.
10.
Which statement is false?
a. When light (even monochromatic light) is emitted by a source, the light waves have no special (phase)
relationship with one another. As a result, the light beam spreads and loses its intensity (brightness)
quickly. This light is said to be incoherent.
b. A laser is a device that produces monochromatic light in which nearly all of the waves are in phase. The
word laser is an acronym for light amplification by stimulated emission of radiation. The color of laser light
depends on the sources that produce the light. Helium-neon lasers, for example, produce red light.
c. The beam produced by a laser spreads very little and is extraordinarily intense. This light is called coherent.
Because of its properties, laser light can be used for a variety of applications, from bar-code scanning to eye
surgery.
d. The light from a laser and a flashlight are both in phase, the laser has more energy and thus is brighter.
SUMMARY
Diffraction and interference can be demonstrated by passing light through a single- or double-slit arrangement.
These devices can be used to measure the wavelength of light. Interference also occurs with the reflected light from
thin films and is responsible for the colors seen on soap bubbles and oil slicks.
If monochromatic light is generated so that all of the waves have a constant phase relationship, the light is coherent.
Lasers produce intense beams of coherent light.