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Part I. [43 Points] Please be sure to mark all answers for Multiple Choice problems on your scantron sheet!!
A two-slit experiment is setup as shown to
First maxima (P)
the right. The point P, a bright spot, is the
first 2-slit interference maximum above the
central spot.
C
1. [3 Points] Which of the labeled lengths
(A, B, C, or D) is very close to a single
B
wavelength?
D
S
A. A
A
B. B
C. C
D. D
E. S
2. [5 Points] If that first 2 slit maximum (P)
occurs at 3.9 degrees, at what approximate angle does the 8th maxima occur?
A. 24 degrees
B. 28 degrees
C. 33 degrees
D. Not enough information is given to calculate this.
E. No 8th maxima occurs
3. [5 Points] If the first diffraction minimum occurs at the 4th two slit minimum, then the relationship
between the slit separation, D, and the slit width S, is:
A. 𝐷 = 𝑆
5
B. 𝐷 = 2 𝑆
7
C. 𝐷 = 2 𝑆
9
D. 𝐷 = 2 𝑆
E. Not enough information to determine.
4. [5 Points] A speck of dust with a mass of 4.0×10−7 g is traveling with some
velocity 𝑣 and diffracts through a small hole and then travels to a screen
45 cm away. If the speck of dust is to form a matter wave whose diffraction
pattern we can see, it must have some observable wavelength. How long
will it take for the speck of dust to travel from the hole to the screen,
assuming it only needs to travel 45 cm (in a straight line), if its effective
wavelength is 0.5 mm?
A.
B.
C.
D.
E.
1.4×10−21 years
4.3×1012 years
4.3×1015 years
2.7×1015 years
3.4×1022 years
Physics 123 A&B, Fall 2016
.
𝑣
45 cm
Midterm Exam 2, page 1
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5. [5 Points] You excite an unknown gas, and it emits light. Using a 2000 slit diffraction grating with a
spacing 𝑑 between the slits, you observe lines on a distant screen. What answer best represents everything
that will happen to the locations, size, and brightness of the lines if the number of slits is reduced to 1000,
but the spacing 𝑑 is kept the same?
A. Nothing. They are identical.
B. They are identical other than being dimmer by a factor of 4, and the width of the lines remains the
same.
C. They are identical other than being dimmer and the width of the lines is larger.
D. The lines move closer to the central maximum, and are dimmer, and are the same size.
E. The lines move further from the central maximum, and are dimmer, and are the same size.
6. [5 Points] A telescopes main aperture has an opening of 11 m (it is a BIG telescope) for red light (𝜆 =
400 nm). What is the diffraction-limited angular resolution?
A.
B.
C.
D.
E.
3.64×10−8 radians
4.44×10−8 radians
8.87×10−8 radians
44.4 radians
88.7 radians
A lens is made of glass (𝑛 = 1.75) and is coated with a magnesium
fluoride coating (𝑛 = 1.41), as shown at right. The coating is meant to
enhance the transmission of light – and is designed to produce zero
MgF coating
reflection for light with wavelength of 481 nm. Treat the lens and
Lens
coating as flat and uniform, and assume the amplitude of the reflected
light from the two surfaces is the same. The lens is in air (𝑛 = 1.0). The
light is incident on the surface on a normal, though it is shown at an
angle.
7. [5 Points] A phase change in the light occurs upon reflection at the following surface or surfaces:
A. Air-MgF boundary
B. MgF-Lens boundary
C. Both the Air-MgF and MgF-Lens boundaries
D. No phase change occurs.
8. [5 Points] What is the minimum thickness of the MgF coating required to prevent 481 nm light from being
reflected?
A. 42.6 nm
B. 85.3 nm
C. 120 nm
D. 171 nm
E. 241 nm
Physics 123 A&B, Fall 2016
Midterm Exam 2, page 2
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9. [5 Points] You are wearing a tee-shirt with HUSKY printed on it. You are
standing at a point P in front of two plane mirrors that are placed together at an
D1
angle of 60°. When you turn and face direction D1 you see a reflection of
60°
yourself with HUSKY printed in reverse. When you turn and face direction D2
you see a reflection of yourself with HUSKY also printed in reverse. For D1
and D2, considering the diagram at the right, how many mirror surfaces does the light reflect from?
A. 1 surface in direction D1, one surface in direction D2
B. 2 surfaces in direction D1, one surface in direction D2
C. 3 surfaces in direction D1, one surface in direction D2
D. 1 surface in direction D1, two surfaces in direction D2
E. 2 surfaces in in direction D1, two surfaces in direction D2.
Physics 123 A&B, Fall 2016
P
D2
Midterm Exam 2, page 3
10. [4 pts.] A person views an o旦iect located at her near point through a converging lens, aS Shown below.
The drawing is to scale, and shows the distance between the o切ect and the eye along with the focal
POints ofthe converging lens. What is the angular magnification as seen by the observer?
十二
(a) 0.5 (b) 0.9 (C) 1.9 (d) 2.2 (e) 3.8
Because the drawing is to scale, We Can determine a fewthings. The djstance from the eye to the object
is 217 mm, andfis lOO mm. Usingthe equation
Mα二鴇雪
Wejustpiugindこ217 mm andf= 100 mm and soIveforMこ=2.17or2.2.
1 1. [4 pts.] A terrestrial telescope ofmagn綿cation +20 is to be constructed with two lenses. The
Objective’s focal length is 500 mm. You must detemine the characteristics ofthe eyepiece lens, and
then answer: How Iong should the telescope be, that is, What is the distance L in the diagram below?
(a)Concave
475mm
(b)Concave
525mm
475mm
(C)Convex
525mm
(d)Convex
(e)Notenough
informationto determine.
In orderto make a terrestriaI (image is upright) telescope with oniy one eyepiece, the lens must be
concave′ ru-ingoutanswerscand d" Togeta magnification of20′We uSeMこ-gandso-vefo帝
giving us a focaI length of2与mm forthe eyepiece.
To find the tube length, rememberthat for a GaiiIean teiescope the focal point ofthe eyepiece is pIaced
On the focal point ofthe objective, With the eyepiece being piaced inside the objective focal point. This
meansthetube length is500mm-2与mm, Or47与mm.
12. [4 pts.] An experiment is set up with an optical bench as shown below. Rays are drawn to Iocate the
image of the lamp made by the convex side of the three sided mirror. Which of the labeled dots is
CIosest to the image position?
(a) A
(b) B
(e) E
The top rayfrom the light source is incident on the convex mirror surface perpendicuiarly, SO it appears
to havecomefrom a lineconnectingpointCto point E. This ruIesoutA, B,and D. We needtofigure out
Which point, eitherC or E is cIosestto the image position. Usingthe iower ray and drawing a tangentto
the mirrorsurface where that rav strikesthe mirror, yOu uSe Gi = G, and reflectthe ray, Drawing a dashed
line backthrough the mirror, We See that it passes over point E, makingthatthe image location,
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[20 points total] The photograph at right shows the pattern created
on a distant screen when monochromatic light from a laser is
incident on two identical, very narrow slits, S1 and S2, separated by
a distance d.
K
2-slit
pattern
A. [5 pts] Determine the phase difference, Δ𝜑, at points K, L, and
M on the screen due to the light from slits S1 and S2. Explain.
Δ𝜑 at point K
Δ𝜑 at point L
L M
Center of screen
Δ𝜑 at point M
4𝜋 (or zero)
2𝜋 (or zero)
𝜋
Point K is the second maximum from the center. The path length difference from slits S1 and S2 to
point K is 2λ and the phase difference is 4𝜋 (or zero). Similarly, the path length difference to point L
is λ and the phase difference is 2𝜋 (or zero). Point M is the first minimum from the center. The path
length difference to point M is λ/2 and the phase difference is 𝜋.
λ
The path length difference from slits S1 and S2 to point L (∆D12,L) is λ
and the phase difference is 2𝜋, so the path length difference from slits
S2 and S3 to point L is (∆D23,L) λ/2 and the path difference is 𝜋, as shown in the
phasor diagram. The sum of the three phasors would have a magnitude for a
single phasor. For a principal maximum, all three phasors should be in the
same direction, thus it would be something in between at point L.
λ/2
d
To
po
int
B. [5 pts] After the third slit is added, will point L be a point of maximum
constructive interference (a principal maximum), a point of zero
intensity (a minimum), or something in between? Justify your answer
both in words and with a phasor diagram.
L
Now a third slit (S3) of equal width is added. It is a distance d/2 to the right of slit S2, as shown in the
magnified view at right.
d/2
S1,L
S3,L
S2,L
C. [5 pts] After the third slit is added, will point M be a point of maximum constructive interference, a
point of zero intensity, or something in between? Explain.
Since point M was previously a point of zero intensity, adding another slit will cause point M to have
an intensity equal to that for a single slit, regardless of where the slit is added. Thus, the intensity at
point M is something in between the intensity for a point of maximum constructive interference and
zero intensity.
K
D. [5 pts] Now slit S2 is covered as shown at right. Will point K be a point of maximum constructive
interference, a point of zero intensity, or something in between?
Explain.
The path length difference from slits S1 and S2 to point K (∆D12,K) is 2λ,
so the path length difference from slits S1 and S3 to point K (∆D13,K) is
3λ. Thus, light from slits S1 and S3 is in phase at point K, so point K
will be a point of maximum constructive interference.
Physics 123A&B, Autumn 2016
Exam 2
3λ
2λ
d
To
po
int
IV.
d/2
WO-UWA123AB164T-E2(MSI,PHZ)Sol.docx