Phy 1112K, Spring, 2004, Final
Name:_______________________,
Number _______
Multiple Choice (2 point each)
c 1.
c
d
b
b
b
c
b
d
The primary coil of a transformer has 100 turns and its
secondary coil has 400 turns. If the ac current in the
secondary coil is 2 A, what is the current in its primary
coil?
a. 2 A
b. 8 A
c. 1/2 A
d. 4 A
2. The transverse nature of electromagnetic waves is apparent
because
a. they are electric in nature.
b. they are magnetic in nature.
c. they can be polarized.
d. they are electromagnetic in nature.
3. A person approaches a plane mirror at a speed of 4 m/s. How
fast does he approach his image?
a. 4 m/s
b. 5 m/s
c. 6 m/s
d. 8 m/s
4. How tall must a plane mirror be in order for you to be able to
see your full image in it?
a. the same height as you.
b. half of your height.
c. 3/4 of your height.
d. twice your height.
5. When the reflected light is totally polarized, the angle
between the reflected ray and the refracted ray is
a. 180o
b. 90o
c. 45o
d. 60o
6. Which of the following is a correct statement? For a real
object,
a. a concave mirror always produces a real image.
b. a convex mirror always produces a virtual image.
c. a concave mirror always produces a virtual image.
d. a convex mirror always produces a real image.
7. Which of the following is a correct statement? For a real
object,
a. a converging lens always produces a real image.
b. a converging lens always produces a virtual image.
c. a diverging lens always produces a virtual image.
d. a diverging lens always produces a real image.
8. When light passes from air to glass, it
a. bends toward the normal without changing speed.
b. bends toward the normal and slows down.
c. bends toward the normal and speeds up.
d. bends away from the normal and slows down.
9. The lens in a person's eye is too thick. The condition that
this person has is called
a. farsightedness
b. astigmatism
c. chromatic aberration
d. nearsightedness
a 10. In the two-slit experiment, for the condition of bright
fringes, the value of m = +4 corresponds to a path difference
of
a. 4λ
b. 3λ
c. 2λ
d. λ
d 11. If the distance between the slits and the screen is increased
in Young's two-slit experiment, which one of the following
statements is true of the interference pattern?
a. The distance between the minima stays the same.
b. The distance between the minima decreases.
c. The distance between the maxima stays the same.
d. The distance between the maxima increases.
b 12. When light travels from a smaller index of refraction towards
a larger index of refraction, there is no phase change upon
reflection at the boundary.
a. true
b. false
c. it depends
b 13. Which one of the following phenomena shows the wave nature of
light?
a. reflection
b. interference
c. photoelectric effect
d. all of the above
c 14. Which one of the following phenomena shows the particle nature
of light?
a. reflection
b. interference
c. photoelectric effect
d. all of the above
b 15. Modern physics considers that
a. physical quantities are continuous.
b. physical quantities are discrete.
c. physical quantities can precisely measured simultaneously.
c 16. Which one of the following is true regarding the energy of the
photon?
a. It depends upon the intensity.
b. It depends upon its amplitude.
c. It depends upon its frequency.
d. It depends upon its velocity.
a 17. The wavelength of a light beam is doubled. Which one of the
following is correct for the momentum of photons for that
light beam?
a. It is halved.
b. It stays the same.
c. It is doubled.
d. It is quadrupled.
d 18. In the photoelectric experiment, the work function depends on
a. the frequency of the incident light.
b. the wavelength of the incident light.
c. the intensity of the incident light.
d. The target material.
b 19. If the position of an electron is measured very precisely
there is an uncertainty in measuring it
a. kinetic energy.
b. momentum.
c. potential energy.
d. None of the other answers is correct.
b 20. What happens to the frequency of the scattered X-rays photon
in the Compton scattering experiment?
a. Stays the same.
b. It decreases
c. Not enough information.
d. It increases
Problems (60 points)
1.
A step-up transformer has 25 turns on the primary coil and 500
turns on the secondary coil. If this transformer is to produce
an output of 4800 V with a 12-mA current, what input current
and voltage are needed? (7 points)
Ip = Is (
Ns
500
) = (12 × 10 −3 A)(
) = 0.24 A
Np
25
2.
I0
3.
4.
Np
25
) = 240 V
Ns
500
Unpolarized light passes through two polarizers whose
transmission axes are at an angle of 30o with respect to each
other. What fraction of the incident intensity is transmitted?
(7 points)
1
I1 = I0
2
1
I2 = I1 cos2 θ = I0 cos2 θ
2
I2
1
2
=
c o s 3 0 .0 ° = 0.375
Vp = Vs (
) = (4800 V)(
2
Draw a ray diagram for each of the following cases. (8 points)
(a)
An object is placed 6 cm in front a converging mirror of focal length 4 cm.
(b)
An object is placed 6 cm in front a converging lens of focal length 4 cm.
(c)
An object is placed 6 cm in front a diverging mirror of focal length 4 cm.
(d)
An object is placed 6 cm in front a diverging lens of focal length 4 cm.
(See examples in the book)
A converging lens (f = 12.0 cm) is located 30.0 cm to the left of a diverging lens (f = -6 cm). A postage
stamp is placed 36 cm to the left of the converging lens (see figure).
(a) Locate the final image of the stamp relative to the diverging lens. (5 points)
(b) Find the overall magnification. (1 point)
(c) Is the final image real or virtual? (1 point)
(d) With respect to the original object, is the final image upright or inverted? (1 point)
(e) With respect to the original object, is the final image larger or smaller? (1 point)
f = - 6 cm
f = 12 cm
36 cm
30 cm
f = 12 cm
36 cm
First, find the image distance for the first lens:
f = +12 cm
d0 = +36 cm
di = [f x d0] / [d0 -f] = (12 cm)(36 cm) / (36 - 12) cm
= (12 x 36 / 24) cm = +18 cm
The image is 18 cm to the right of the first lens. From the diagram it is obvious that the image is
inverted, real and reduced in size.
This first image is the object for the diverging lens which is now located 12 cm from the first image
position.
f = - 6 cm
X-Position of final image
F
X
12 cm
That is, d02 = +12 cm and f = -6 cm.
di2 = [f x d02] / [d02 - f] = (-6 cm)(12 cm) / (12 - -6) cm
= (-6 x 12 / 18) cm = -4 cm
di2 is negative so image is to the left of the diverging lens. This can be seen in the ray diagram. The
final image is also inverted and virtual.
(b)
Overall magnification MT = M1 x M2 = (-di1 / d01) x (-di2 / d02)
= (- 18 / 36) x (- -4 / 12) = (-3 / 2) x (1 / 9)
= - 1 /6
(c)
Final image is virtual.
(d)
Final image is inverted because the total magnification is negative.
(e)
Final image is reduced in size by a factor of 6.
5.
A college professor can see objects clearly only if they are between 70 and 500 cm from his
eyes. His optometrist prescribes bifocals that enable him to see distant objects clearly through
the top half of the lenses and read students papers at a distance of 25 cm through the lower half.
What are the powers of the top and bottom lenses? (7 points)
T op:
P =
do = ∞ ,
d i = − 5 0 0 c m = − 5 .0 m ( i m a g e o n o b je c t s id e ) .
1
1
1
1
1
=
+
=
+
=
f
do
di
∞
− 5 .0 m
B o tto m : d o = 2 5 c m = 0 .2 5 m ,
P =
6.
1
1
+
=
0 .2 5 m
− 0 .7 0 m
− 0 .2 0 D .
d i = − 7 0 c m = − 0 .7 0 m ( i m a g e o n o b je c t s id e ) .
+ 2 .6 D .
Monochromatic light passes through two slits separated by 0.0234
mm. If the angle to the third maximum above the central is 3.51o,
what is the wavelength of the light? (7 points)
λ
λ 3λ
= (3) =
d
d
d
1
1
λ = d sin θ = (0.0234 × 10 −3 m)sin 3.51° = 478 nm
3
3
sin θ = m
7.
A film of oil with index of refraction 1.5 is spread on water whose index of refraction is 1.33.
Calculate the minimum thickness of the film for which green light of wavelength 520 nm is
reflected constructively. (7 points)
There is a half wavelength phase change for ray 1 as ray 1 is reflected at the air-gasoline
interface. So 2t = mλ
λf is the condition for destructive interference between rays 1 and 2.
And 2t = (m+1/2)λ
λf is the condition for constructive interference between rays 1 and 2.
For constructive interference, the minimum thickness is for m = 0
So
2t = 1/2λ
λf
or t = λf / 4 = (520 nm / 1.5)/4 = 346.67 nm / 4 = 86.66 nm
8.
The maximum wavelength that can give photoelectrons from a
platinum surface is 190 nm. When light of wavelength 140 nm
shines on the surface what is the maximum speed of the ejected
electrons.(mass of electron = 9.1x10-31 kg) (8 points)
1240(nm ⋅ eV )
= 653
. eV
190(nm)
1240(nm ⋅ eV )
= 886
E = hc / λ =
. eV
190(nm)
( KE ) max = E − W0 = 886
. eV − 653
. eV = 2.33 eV
W0 =
1 2
= 91
( KE ) max = mvmax
. × 10−31 kg
2
vmax =
2 × 2.33 eV × 16
. × 10−19
91
. × 10−31 kg
j
eV = 91
. × 105 m / s