Week 11 Chapter 16:
1. Suppose the parallel-plate capacitor shown below is accumulating
charge at a rate of 0.03 C/s. What is the induced magnetic field at a
distance of 10 cm from the capacitor? (6E-8 T)
2. An electromagnetic wave has a frequency of 450 MHz. What is its
wavelength in a vacuum? (0.666 m)
3. A radio station broadcasts at a frequency of 760 kHz. At a receiver
some distance from the antenna, the maximum magnetic field of
the electromagnetic wave detected is 4.75*10^-11 T. What is the
maximum electric field? (0.01425 V/m)
4. At what distance does a 100 W lightbulb produce the same
intensity of light as a 75 W lightbulb produces 10 m away?
Assume both have the same efficiency for converting electrical
energy in the circuit into emitted electromagnetic energy. (11.4 m)
5. A 175 W lightbulb emits 5% of its energy as electromagnetic
radiation. What is the magnitude of the average Poynting vector 10
m from the bulb? (0.00696 W/m^2)
6. A small helium-neon laser has a power output of 2.5 mW. What is
the electromagnetic energy in a 2.1 m length of the beam?
(1.75E-11 J)
7. What is the intensity of an electromagnetic wave with a peak
electric field strength of 475 V/m? (299 W/m^2)
8. An AM radio transmitter broadcasts 47.2 kW of power uniformly
in all directions. Assuming all of the radio waves that strike the
ground are completely absorbed and that there is no absorption by
the atmosphere or other objects, what is the intensity 30 km away?
(Hint: Half the power will be spread over the area of a hemisphere)
(4.172E-6 W/m^2)
9. A 2.8 m diameter satellite dish receives TV signals that have a
maximum electric field strength (for one channel) of 8.64 uV/m.
What is the intensity of this wave? (9.909E-14 W/m^2)
10.A helium-neon laser commonly used in physics laboratories has a
power output of 0.42 mW. If such a laser beam is projected onto a
circular spot 1.46 mm in diameter, what is its intensity? (251
W/m^2)
11.A laser that emits pulses of UV lasting 3 ns has a beam diameter of
1.55 mm. If each burst contains an energy of 3.5 J, what is the
length in the space of each pulse? The speed of light is c = 3 x 10^8
m/s. (0.9 m)
12.An industrial laser is used to burn a hole through a piece of metal.
The RMS value of the electric field E = 4.7E6 V/m. What is the
RMS value of the magnetic field? The permittivity of free space is
e = 8.85 x 10^-12 F * m-1. (0.0156 T)
13.An industrial laser is used to burn a hole through a piece of metal.
The average intensity of the light is Save = 4.6E9 W/m^2. What is
the RMS value of the electric field? (1316275 V/m)
14. What is the intensity of an electromagnetic wave with a peak
electric field strength of 800 V/m? (849 W/m^2)
Chapter 1:
1. A light ray with a wavelength of 630 nm enters a block of plastic from
the air at an incidence angle of 37.4 deg. The angle of refraction is 22.7
deg. What is the speed of light inside the plastic? The speed of light is c =
3x10^8 m/s. (1.906 x 10^8 m/s)
2. The refractive index of a transparent material can be determined by
measuring the critical angle when it is in the air. If the critical angle is
theta = 33.9 deg, what is the index of refraction of the material? (1.7929)
3. What is the speed of light in water? The refraction index of the water is
1.33 (2.255E8 m/s)
4. Calculate the index of refraction for a medium in which the speed of light
is 2.012 x 10^8 m/s. (1.49)
5. A light beam in the air is incident on the surface of a pond, making an
angle of 20 deg with respect to the surface. What is the angle of
refraction? The reflecrtive index of water is 1.33, and air is 1.00. (44.95
deg)
6. When a light ray crosses from water into the grass, it emerges at an angle
of 30 deg with respect to the normal of interface. What is its angle of
incidence? The refractive index of water is 1.33, and for glass is 1.52.
(34.85 deg)
7. A pencil flashlight submerged in water sends a light beam toward the
surface at an angle of incidence of 30 deg. What is the angle of refraction
in the air? The refraction index of water is 1.33 and that of air is 1. (41.68
deg)
8. Light rays from the Sun male a 30 deg angle to the vertical when seen
from below the surface of a body of water. At what angle above the
horizon is the Sun? (48.32 deg)
9. Suppose you are using total internal reflection to make an efficient corner
reflector. If there is air outside and the incident angle is 45 deg, what must
be the minimum index of refraction of the material from which the
reflector is made? (1.414)
Chapter 2:
1. Calculate the focal length of a mirror formed by the shiny back of a spoon
that has a 3 cm radius of curvature. (0.015 m)
2. A doctor examines a mole with a 15 cm focal length magnifying glass
held 13.5 cm from the mole. Where is the image? (-1.35 m)
3. A doctor examines a mole with a 15 cm focal length magnifying glass
held 13.5 cm from the mole. What is its magnification? (10)
4. Suppose your 50 mm focal length camera lens is 51 mm away from the
film in the camera. How far away is an object that is in focus? (2.55 m)
5. Suppose your 50 mm focal length camera lens is 51 mm away from the
film in the camera. What is the height of the object if its image is 2 cm
high? (1)
6. What is the focal length of magnifying glass that produces a
magnification of 3 when held 5 cm from an object, such as a rare coin?
(0.075 m)
7. An object of height 3 cm is placed 5 cm in front of a converging lens of
focal length 20 cm and observed from the other side. Where and how
large is the image? (-6.66 cm and 0.04 m)
8. An object of height 3 cm is placed 5 cm in front of a diverging lens of
focal length 20 cm and observed from the other side. Where and how
large is the image? (-4 cm and 2.4 cm)
9. The print in many books averages 3.5 mm in height. How high is the
image of the print on the retina when the book is held 30 cm from the
eye? (-0.000233 m)
10. What is the magnification of a magnifying lens with a focal length of 10
cm if it is held 3 cm from the eye and the object is 12 cm from the eye?
(3.96)
11. For a normal, relaxed eye, a magnifying glass produces an angular
magnification of 4. What is the largest magnification possible with this
magnifying glass? (5)
12. What magnification is produced by a 0.15 cm focal length microscope
objective that is 0.155 cm from the object being viewed? (1.387)
13. Where does an object need to be placed relative to a microscope for its
0.5 focal length objective to produce a magnification of -400? (0.00501
m)
Chapter 3:
1. What is the wavelength of light falling on double slits separated by 2 um
if the third-order maximum is at an angle of 60 deg? (5.77E-7 m)
2. What is the highest-order maximum for 400 nm light falling on double
slits separated by 25 um? (62.5)
3. Find the largest wavelength of light falling on double slits separated by
1.2 um for which there is a first-order maximum. Is this in the visible part
of the spectrum? (1.2E-6 m)
4. What is the smallest separation between two slits that will produce a
second-order maximum for 720 nm red light? (1.44E-6 m)
5. If the first-order maximum for monochromatic light falling on a double
slit is at an angle of 10 deg, at what angle is the second-order maximum?
(20.32 deg)
6. If the first-order maximum for monochromatic light falling on a double
slit is at an angle of 10 deg, what is the angle of the first minimum? (4.98
deg)
7. If the first-order maximum for monochromatic light falling on a double
slit is at an angle of 10 deg, what is the highest-order maximum possible
here? (5)
8. Calculate the distance between fringes for 633 nm light falling on double
slits separated by 0.08 mm, located 3 m from a screen. (2.37 E-2 m)
9. The distance between fringes for 633 nm light falling on double slits
separated by 0.08 mm, located 3 m from a screen. What would be the
distance between fringes if the entire apparatus were submersed in water,
whose index of refraction is 1.33? (1.78 E-2 m)
10.Find the wavelength of light that produces fringes 7.5 mm apart on a
screen 2 m from double slits separated by 0.12 mm. (450E-9 m)
Chapter 4:
1. At what angle is the first minimum for 550-nm light falling on a single
slit of width 1.00 um? (33.4 deg)
2. How wide is a single slit that produces its first minimum for 633 nm light
at an angle of 28 deg? (1.35E-6 m)
3. What is the width of a single slit that produces its first minimum at 60
deg for 600-nm light? (6.93E-7 m)
4. Find the wavelength of light that has its third minimum at an angle of
48.6 deg when it falls on a single slit of width 3 um. (7.5E-7 m)
5. Sodium vapor light averaging 589 nm in wavelength falls on a single slit
of width 7.5 um. At what angle does it produce its second minimum?
(9.04 deg)
6. Find the angle between the first minima for the two sodium vapor lines,
which have wavelengths of 589.1 and 589.6 nm, when they fall upon a
single slit of width 2 um. (0.015 deg)
7. If the separation between the first and second minima of a single-slit
diffraction pattern is 6 mm, what is the distance between the screen and
the slit? The light wavelength is 500 nm, and the slit width is 0.16 mm.
(1.92 m)
8. A monochromatic light of wavelength 589 nm incident on a double slit
with slit width 2.5 um and unknown separation results in a diffraction
pattern containing nine interference peaks inside the central maximum.
Find the separation of the slits. (2.25E-5 m)
9. When a monochromatic light of wavelength 430 nm incident on a double
slit of slit separation 5 um, there are 11 interference fringes in its central
maximum. How many interference fringes will be in the central
maximum of a light of wavelength 632.8 nm for the same double slit?
(11)
Extra Questions
1. X-rays of wavelength 0.103 nm reflect off a crystal, and a second-order
maximum is recorded at a Bragg angle of 25.5 deg. What is the spacing
between the scattering planes in this crystal? (2.39E-10 m)
2. An X-ray scattering experiment is performed on a crystal whose atoms
form planes separated by 0.440 nm. Using an X-ray source of wavelength
0.548 nm, what is the angle (with respect to the planes in question) at
which the experimenter needs to illuminate the crystal in order to observe
a first-order maximum? (38.5 deg)
3. The structure of the NaCl crystal forms reflecting planes 0.541 nm apart.
What is the smallest angle, measured from these planes, at which X-ray
diffraction can be observed if X-rays of wavelength 0.085 nm are used?
(4.5 deg)
4. On a certain crystal, a first-order X-ray diffraction maximum is observed
at an angle of 27.1 deg relative to its surface, using an X-ray source of
unknown wavelength. Additionally, when illuminated with a different this
time of known wavelength 0.137 nm, a second-order maximum is
detected at 37.3 deg. Determine the spacing between the reflecting planes
and the unknown wavelength. (0.29E-9 m and 0.137E-9 m)
5. The first-order Bragg angle for a certain crystal is 12.1 deg. What is the
second-order angle? (24.8 deg)