1.
1. A plane wave of wavelength is incident on a barrier in which there is an opening of diameter d. (a) When
, the rays continue in a straight-line path, and the ray approximation remains valid. (b) When
, the rays
spread out after passing through the opening. (c) When
, the opening behaves as a point source emitting
spherical waves.
2. For light and electromagnetic waves to reach the earth from the distant galaxies, it takes a long period of time to
do so even the fact that such electromagnetic waves travel at the fastest speed ever known (
).
Most galaxies are located at distances measured in “Light year” from the earth.
Light-Year, in astronomy, unit of length sometimes used to measure vast distances. It is equivalent to the
distance that light travels in a mean solar year. At the rate of approximately 300,000 km/sec (186,000 mi/sec), a
light-year is equal to 9,461,000,000,000 km (5,880,000,000,000 mi).
For example, light reaching us from the sun (at 149,600,000 km away from earth) takes about 8 minutes to
traverse the sun – earth distance. In so doing, this light is not of the current moment but represents the past
eight minutes of the sun.
3.
a) The frequency f of the He-Ne red laser of wavelength
is calculated as follows:
b) When light travels in air or vacuum it has a wavelength and speed c, but once it inters a medium of different
optical density such as glass which is more dense than air, its speed is slowed down and becomes v with
wavelength . The frequency remains fixed. The ratio n=c/v is the refractive index of the medium. Therefore, the
wavelength
is
given
by:
c) The speed v is calculated as follows:
⁄
⁄
4. The refractive index of the crown glass is 1.52 and to calculate the angle of reflection
one needs to find the
angle of incidence . By applying the Snell’s law of refraction at the air – crown glass media interface ever since
the angle of refraction Is given, the angle of incidence can be evaluated:
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2.
According to the law of reflection, the reflected
ray, the reflected ray, and the normal all lie in
the same plane
5.
a) The refractive index of the corn syrup n2 is calculated by applying Snell law of refraction at the water – corn
( )
syrup interface as follows:
b) The
wavelength
in
the
medium
is
lesser
than
that
in
the
vacuum:
c) The frequency of light as it enters the medium remains unchanged (fixed always for the particular light) and is
calculated as:
d) The speed of light v in the medium is:
6.
a) The speed of light
(
)(
)
in the flint glass medium is:
b) In water, n=1.33 so light speed will be:
c) For cubic zirconia, the refractive index is 2.2 and the speed of light waves will be:
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3.
7. Applying Snell’s law of refraction at the water – transparent substance interface:
[
][
]
8. Applying Snell’s law of refraction at the first air – glass interface to find the angle of refraction as follows:
[
From the figure at the right, applying Snell’s law at the second glass –
air interface:
]
[
]
𝜃𝑖
𝑛 𝑎𝑖𝑟
𝑛 𝑔𝑙𝑎𝑠𝑠
𝜃𝑡
[
]
[
]
It is obvious that the light enters and exits the flat block of glass
with the same angle of 30 degrees with the normal to the surface.
However, the direction of propagation of light rays is displaced by a
distance d with respect to the incident rays.
𝜃𝑖
𝜃𝑡
d
9. A transverse wave is one in which the elements of the medium move in a direction perpendicular to the
direction of propagation. An example is a wave on a taut string. Also, the electromagnetic waves are transverse.
Longitudinal wave is one in which the elements of the medium move in a direction parallel to the direction of
propagation. Sound waves in fluids are longitudinal.
10.
Sound waves
Sound waves are longitudinal in which the
elements of the medium move in a direction
parallel to the direction of propagation.
Sound waves and travel through a
compressible medium with a speed that
depends on the elastic and inertial properties
of that medium.
By definition, the propagation of mechanical
disturbances—such as sound waves, water
waves, and waves on a string—requires the
presence of a medium.
Light waves
Light waves are transverse, i.e., the components of the
electric and magnetic fields of plane electromagnetic
waves are perpendicular to each other and perpendicular
to the direction of wave propagation.
Electromagnetic waves (unlike mechanical waves) can
travel through empty space at the speed of light c
The waves carry energy. The rate of flow of energy crossing
a unit area is described by the Poynting vector S,
Electromagnetic waves carry momentum and hence exert
pressure on surfaces.
The electromagnetic spectrum includes waves covering a
broad range of wavelengths, from long radio waves at
more than 104 m to gamma rays at less than 10-14 m.
11. Electromagnetic waves are generated by oscillating electric charges. The waves consist of oscillating electric and
magnetic fields at right angles to each other and to the direction of wave propagation. Thus, electromagnetic
waves are transverse waves. The waves radiated from the oscillating charges can be detected at great distances.
Furthermore, electromagnetic waves carry energy and momentum and hence can exert pressure on a surface.
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4.
12. Astonishingly, Maxwell’s equations also predict the existence of electromagnetic waves that propagate through
space at the speed of light c. The Ampère–Maxwell law predicts that a time-varying electric field produces a
magnetic field, just as Faraday’s law tells us that a time-varying magnetic field produces an electric field.
Therefore, not all current – carrying conductors are able to emit electromagnetic waves. Only when there is a
time – varying of current in a conductor there is an electromagnetic wave.
13. Radio waves (frequencies of about 107 Hz) are electromagnetic waves produced by oscillating currents in a radio
tower’s transmitting antenna. Light waves are a high-frequency form of electromagnetic radiation (about 1014
Hz) produced by oscillating electrons in atoms.
14. The magnitudes of E and B in empty space are related by the expression:
Electric and magnetic fields are measured in different units, however, so they cannot be directly compared. The
electric and magnetic fields contribute equally to the energy of the wave. That is, the instantaneous energy
density associated with the magnetic field of an electromagnetic wave equals the instantaneous energy density
associated with the electric field. Hence, in a given volume the energy is equally shared by the two fields.
15. The frequency f (in Hz = cycles/second) of the electromagnetic wave can be calculated as given below:
16.
17.
a) For a person of 175 - cm average tall:
b) For a typical paper of 0.1 mm, the wavelength and frequency of such waves will be:
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5.
18.
a) The wavelength
follows:
of electromagnetic wave in free space of frequency
b) For electromagnetic wave of frequency
is evaluated as
, the wavelength is calculated as:
19. Electromagnetic waves, including light, travel in free space with speed of
where is the wavelength in
vacuum and is the frequency. When propagating in medium other than free space, light travels at a lower
speed of
As light travels from one medium to another, its frequency does
not change but its wavelength does. To see why this is so, consider the Figure to
the right. Waves pass an observer at point A in medium 1 with a certain
frequency and are incident on the boundary between medium 1 and medium 2.
The frequency with which the waves pass an observer at point B in medium 2
must equal the frequency at which they pass point A. If this were not the case,
then energy would be piling up at the boundary. Because there is no mechanism
for this to occur, the frequency must be a constant as a light ray passes from one
medium into another. Therefore, because the relationship
must be valid
in both media and because
, we see that
Because
, it follows that
.
20.
a) The
frequency
So,
the
number of wavelengths you are away from the station will be
b) For the FM band, the frequency is
and this is equivalent to a wavelength of
21. For people sitting next to their radios 100 km away from the station, the radio waves take time
to reach them, while the people sitting across the room will hear
the sound waves from the newscaster after a time
.
Apparently, the far away people receive the news first.
22. The shadow length on the vertical wall is:
(
[
]
)
(
)
The same shadow length results when the halving the distance between the point source and the edges of the
meter stick since this causes to half the angle and consequently, tan .
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6.
100
cm
𝜃
582 cm
264 cm
23. The frequency f of the yellow sodium light is:
The wavelength
in
air (or vacuum) changes to when propagating in the medium. For water, it becomes:
24. When light enters a medium, its speed reduces to
glass sheet is calculated by:
. Here,
( ⁄ )
25. The energy of an orange light photon of wavelength
(
)(
(
=(2/3) c and hence the refractive index n of the
(Not 670 nm !!) is calculated as follows:
)
)
26.
27.
28.
29.
30. The shapes are the same, but (a) is a graph of vertical position versus horizontal position while (b) is vertical
position versus time. Figure (a) is a pictorial representation of the wave for a series of particles of the medium—
this is what you would see at an instant of time. Figure (b) is a graphical representation of the position of one
element of the medium as a function of time. The fact that both figures have the identical shape represents
Equation ( )
(
) a wave is the same function of both x and t.
32. See solution of question 35.
33. The critical angle is the angle of incidence of light in the more dense medium (higher refractive index n1) at
which light refracts at an angle of 90 o to the normal in the lesser dense medium (lower refractive index n2).
Thus, the critical angle
a) For diamond, n=2.419,
b) For flint glass, n=1.660,
c) For ice of n=1.309,
34. If the rarer medium is water (n=1.33) other than air (n=1), then the critical angle
replacing the previous value of n2=1 by its value for water, i.e., n2=1.33 as follows:
will be calculated by
a) For diamond, n=2.419,
b) For flint glass, n=1.660,
c) For ice of n=1.309 surrounded by water of n=1.33, no critical angle can be found!! Why??
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7.
35. The maximum refraction angle at which light ray can emerge from the other side of the prism is 90 degrees to
the normal which occurs when light incident at the critical angle given by:
a
b
(
(
(
60 o
f
h
)
))
θ
d
[
i
b
]
g
c
b
42 o
e
d
c
90 o
h
g
This is the smallest incident angle above which light will not emerge from the other side of the prism and light
will totally internally reflected TIR.
36. The distance d that the direction of propagation of light ray will be displaced is given by:
[
(
]
[
]
(
)
)
37. The time interval required for the light to pass through the glass block described in the previous problem is
simply given by:
(
)(
)
38. For a typical glass window of average width of 6 mm, the delay of time results from light being pass through this
glass window is calculated as:
( )(
)
(
39. The difference between the two mean deviation angles, such as
the spectrum. That is:
(
)
(
)
(
)
To calculate the dispersive power
flint glass. Thus:
is a measure of the dispersion of
(
)(
)
one needs to evaluate the index of refraction for yellow light
[
Therefore, the dispersive power
)
]
[
in silica
]
is evaluated as follows:
(
(
)
)
(
(
)
)
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(
(
)
)
Dr. Qahtan Al-zaidi
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