RELATIONS BETWEEN SCIENCE AND TECHNOLOGY
2004 –2005 Semester I
N. Iwamoto ©2004
HOMEWORK NO. 3
Thursday, 17 June 2004
REVIEW QUESTIONS
(1) [Invention of the optical microscope, transmission electron microscope, scanning tunneling microscope
and atomic force microscope]
Who invented the microscope?
When was it?
What did Hans Lippershey and Robert Hooke find by using a optical microscope?
(2) [Characteristics of the convex lens]
(a) Express the lateral magnification, f-number, light collecting power, linear size of the image,
brightness of the image in terms of the diameter, focal length, objective distance, image distance
and the diameter of the lens.
(b) How are the f-number, light collecting power and brightness of the image depend on the diameter
of the lens?
(3) [Human eye and the eye of a mouse]
Compare the human eye and that of a mouse in terms of the focal length, f-number, size of the image
and the brightness of the image.
(4) [Comparison between the telescope and the microscope]
(a) Objective distance (the distance to the object)
(b) Image distance
(c) Tube length
(d) Angular magnification
(e) Lateral magnification
(5) [Particles and waves]
(a) List the phenomena that exhibits that light behaves like a particle.
(b) List the phenomena that exhibits that light behaves like a wave.
(6) [de Broglie relation]
Use the de Broglie relation λ = h/mv to obtain
(a) the wavelength of a 100 g mass traveling at a speed of 150 km/h.
(b) the wavelength of a neutron traveling at a speed of 100 m s-1.
(7) [ħc]
Show that ħc = 197 MeV fm.
(8) [Transmission electron microscope, Scanning tunneling microscope and atomic force microscope]
Compare TEM, STM and AFM.
(9) [X-ray CAT]
Who invented the X-ray CAT?
When was it?
How does it work?
(10) [PET]
Who invented the X-ray CAT?
When was it?
How does it work?
PROBLEMS
(11) [Visual acuity of the human eye]
(a) What is the angular resolution of the human eye empirically? 0.1 mm/30 cm
(b) What is the angular resolution of the human eye from Dawes’s criterion? Use the wavelength of
light 5000Ǻ and the radius of the pupil 0.15-0.8 cm. 5000Ǻ /0.15 cm.
(c) What is the angular resolution of the human eye anatomically? Use the density of the
photoreceptor cells (cones) of 1.6x105 mm-2 and the focal length of the lens 1.69 cm.
(12) [Visual acuity of 1.0]
(a) What does the visual acuity of 1.0 mean?
(b) How big a gap in the Landolt C can one resolve with the visual acuity of 1.0 at a distance of 5 m?
(c) The official 50 ft (15 m) small bore rifle target has a circle of diameter 0.4 cm for 10 points. What
is the visual acuity with which one can resolve this size?
(13) [Pointillism]
When one looks at a painting by Georges Seurat (1859-1891) can one resolve the dots?
Assume that the size of the dot is 0.5 cm and the viewing distance is 3 m.
(14) Transmission coefficient]
Calculate the transmission coefficient for a 10 eV electron in the following cases.
(d) A square barrier of height 11 eV and width 1 Å
(e) A square barrier of height 11 eV and width 10 Å
(f) A square barrier of height 110 eV and width 1 Å
(g) A square barrier of height 110 eV and width 10 Å
(15) [Venus’ transit across the solar disk]
On 8 June 2004, Venus’ transit across the solar disk was observed. It started at about 14:11 and ended
20:19, lasting about six hours. Assume that the Earth and Venus have circular orbits in the same plane
with the orbital radii given below.
(a) Show that the duration of the transit last several hours.
(b) Express the duration in terms of G, MS, DS, rS-V and rS-E, where these quantities are defined
below.
(16) [Duration of a solar eclipse]
(a) Estimate the duration of a solar eclipse. The eclipse starts when the moon’s disk “contacts”
the solar disk and it ends when the disks “detach.”
(b) Express the duration in terms of G, ME, DS, DM, rS-E and rE-M.
(17) [Duration of a lunar eclipse]
(a) Estimate the duration of a lunar eclipse. The eclipse starts when the edge of the Moon’s disk
enters into the shadow of the Earth and it ends when the Moon’s disk comes out of the Earth’s
shadow completely.
(b) Express the duration in terms of G, ME, DE, DM and rE-M.
Use the following symbols and values for Problems 2-4, if necessary.
Mean distance between the Sun and Venus:
Mean distance between the Sun and the Earth:
Mean distance between the Earth and the Moon:
Diameter of the Sun:
Diameter of Venus:
Diameter of the Earth:
rS-V = 0.723 AU = 1.082x108 km
rS-E = 1 AU = 149,598,000 km
rE-M = 384,400 km
DS = 696,000 km
DV = 12,104 km = 0.949 DE
DE = 12,756 km
Diameter of the Moon:
Mean orbital velocity of Venus :
Mean orbital velocity of the Earth:
Mean orbital velocity of the Moon:
Mass of the Sun:
Mass of the Earth:
Newton’s gravitational constant:
DM = 3,476 km
vV = 35.0 km s-1
vE = 29.8 km s-1
vM = 3,680 km/h
MS = 1.989x1030 kg
ME = 5.976x1024 kg
G = 6.637x10-11 m3 kg-1 s-2