物理(波动)光学试卷

南京理工大学课程考试试卷（学生考试用）
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南京理工大学课程考试答案及评分标准
南京理工大学课程考试试卷（学生考试用）
6. Suppose we spread white light out into a fan of wavelengths by means of a diffraction grating and then pass a small select region of that spectrum out through a slit. Because of the slit, a band of wavelengths 1.2 nm wide centered
Determine the frequency bandwidth and the coherence length of this light. (
7. What is the general expression for the separation of the fringes of a Fresnel biprism of
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08A
1. Given the wavefunctions 14sin 2(0.23)x t ψπ=-, and 2[sin(7 3.5)]/
2.5x t ψ=+, determine in each case the values of (a) frequency, (b)wavelength, (c) period, (d)amplitude, (e)phase velocity, and (f) direction of motion. Time is in seconds and x is in meters. (12 points)
2. Write an expression for the E -and B -fields that constitute a plane harmonic wave traveling in the +z-direction. The wave is linearly polarized with its plane of vibration at 450 to the yz -plane. (8 points)
3. A 3.0-V flashlight bulb draws 0.25A, converting about 1.0% of the dissipated power into light
(550nm λ≈). If the beam has a cross-sectional area of 10cm 2 and is approximately cylindrical, (a) How many photons are emitted per second? (b) How many photons occupy each meter of the beam? (c) What is the flux density of the beam as it leaves the flashlight? (346.62610h J s -=⨯⋅) (9 points)
4. A ray of yellow light from a sodium discharge lamp falls on the surface of a diamond in air at 450. If at that frequency 2.42d n =, compute the angular deviation suffered upon transmission. (8 points)
5. A beam of light in air strikes the surface of a smooth piece of plastic having an index of refraction of 1.55 at an angle with the normal of 20.00. The incident light has component E-field amplitudes parallel and perpendicular to the plane-of-incidence of 10.0V/m and 20.0V/m, respectively. Determine the corresponding reflected field amplitudes. (10 points)
6. A magnetic-field technique for stabilizing a He-Ne laser to 2 parts in 1010 has been patented. At 632.8nm, what would be the coherence length of a laser with such a frequency stability? (8 points)
7. An expanded beam of red light from a He-Ne laser (0632.8nm λ=) is incident on a screen containing two very narrow horizontal slits separated by 0.200mm. A fringe pattern appears on a white screen held 1.00m away. (a) How far (in radians and millimeters) above and below the central axis are the first zeros of irradiance? (b) How far (in mm) from the axis is the fifth bright band? (c) Compare these two results. (12 points)
8. One of the mirrors of a Michelson Interferometer is moved, and 1000 fringe-pairs shift past the hairline in a viewing telescope during the process. If the device is illuminated with 500-nm light, how far was the mirror moved? (8 points)
9. Suppose that we have a laser emitting a diffraction-limited beam (0632.8nm λ=) with a 2-mm diameter. How big a light spot would be produced on the surface of the Moon a distance of 337610km ⨯ away from such a device? Neglect any effects of the Earth ’s atmosphere. (7 points)
10. Sunlight impinges on a transmission grating that is formed with 5000 lines per centimeter. Does the third-order spectrum overlap the second-order spectrum? Take red to be 780nm and violet to be 390 nm. (10 points)
11. Imagine that we have randomly polarized room light incident almost normally on the glass surface of a radar screen. A portion of it would be specularly reflected back toward the viewer and would thus tend to obscure the display. Suppose now that we cover the screen with a right-circular polarizer, as shown in the Figure. Trace the incident and reflected beams, indicating their polarization states. What happens to the reflected beam? (8 points)
08A答案
07a
1. Consider a lightwave having a phase velocity of 8310/m s ⨯ and a frequency of
14610Hz ⨯. What is the shortest distance along the wave between any two points that have a
phase difference of 300? What phase shift occurs at a given point in 10-6s, and how many waves have passed by in that time? (12 points)
2. The electric field of an electromagnetic wave traveling in the positive x -direction is given by 00ˆE jsin()cos()E z z kx t πω=-
, (a) Describe the field verbally. (b) Determine an expression for k . (c) Find the phase speed of the wave. (7 points)
3. How many photons per second are emitted from a 100-W yellow lightbulb if we assume negligible thermal losses and a quasi-monochromatic wavelength of 550nm ? In actuality only about 2.5% of the total dissipated power emerges as visible radiation in an ordinary 100-W lamp. (346.62610h J s -=⨯⋅) (8 points)
4. A laserbeam impinges on an air-liquid interface at an angle of 550. The refracted ray is observed to be transmitted at 400. What is the refractive index of the liquid? (7 points)
5. Light is incident in air perpendicularly on a sheet of crown glass having an index of refraction of 1.522. Determine both the reflectance and the transmittance. (12 points)
6. Imagine that we chop a continuous laserbeam (assumed to be monochromatic at
0632.8nm λ=) into 0.1-ns pulses, using some sort of shutter. Compute the resultant
linewidth λ∆, bandwidth, and coherence length. Find the bandwidth and linewidth that would result if we could chop at 1015Hz . (8 points)
7. With regard to Young ’s Experiment, derive a general expression for the shift in the vertical position of the m th maximum as a result of placing a thin parallel sheet of glass of index n and thickness d directly over one of the slits. Identify your assumptions. (10 points)
8. Suppose we place a chamber 10.0cm long with flat parallel windows in one arm of a Michelson Interferometer that is being illuminated by 600-nm light. If the refractive index of air is 1.00029 and all the air is pumped out of the cell, how many fringe-pairs will shift by in the process? (10 points)
9. If you peered through a 0.75-mm hole at an eye chart, you would probably notice a decrease in visual acuity. Compute the angular limit of resolution, assuming that it ’s determined only by diffraction; take 0550nm λ=. Compare your results with the value of
41.710rad -⨯, which corresponds to a 4.0-mm pupil. (10 points)
10. Light having a frequency of 144.010Hz ⨯ is incident on a grating formed with 10000 lines per centimeter. What is the highestorder spectrum that can be seen with this device? Explain. (8 points)
11. A Babinet compensator is positioned at 450 between crossed linear polarizers and is being illuminated with sodium light. When a thin sheet of mica (indices 1.599 and 1.594) is placed on the compensator, the black bands all shift by 1/4 of the space separating them. Compute the retardance of the sheet and its thickness. (8 points)
1. Solution:
814/310/5100.6c m λνμ==⨯⨯= 83/310/60510c km λν==⨯=⨯
2. Solution:
The number of waves is 0/AB λ. With the glass in place, there are 0()/AB L λ- waves in vacuum and an additional /L λwaves in glass for a total of 00(/)(1/1/)AB L λλλ-. The difference in number is 0(1/1/)L λλ-, giving a phase shift of φ∆ of 2π for each wave; hence , 0002(1/1/)2(/1/)2/22000L L n L πλλπλλπλπ-=-==.
3. Solution:
(a) The phase angle is retarded by an amount (2/)2/n y y πλπλ∆-∆ or (1)/n y c ω-∆. Thus
0exp [(1)//]p E E i t n y c y c ω=--∆- or 0exp[(1)/]exp (/)p E E i n y c i t y c ωω=--∆- (b) Since 1x e x ≈+ for small x, if 1n ≈ of 1y ∆ , exp[(1)/]1(1)/i n y c i n y c ωω--∆≈--∆ and since exp(/2)i i π-=-, (1)(/)exp(/2)p u u E E n y E c i ωπ=+-∆-
4. Solution:
/t i t i r n n n n -+ . Air-water: 4/31
1/70.144/31
r -=
==+. Air-crown glass:
3/21
1/50.203/21
r -=
==+.
More reflectance for glass. 2/r i I I R r ==.
Air-water: 2(1/7)0.02R ==. Air-crown glass: 2(1/5)0.04R ==
5. Solution:
/21sin sin i
t t
i n n θθθθ==
/2/1sin sin t i n n θθ=
/21sin sin t i n n θθ= and /t i i θθ=
__
/cos AB d t =θ ___
/)sin(AB a t i =-θθ t t i d
a
θθθcos )sin(=
- a d t t i =-θθθcos )
sin(
6. Solution:
99//(1.210)/(50010)0.0024m m ννλλ--∆=∆=⨯⨯=
c νλ=, so 8914/(310/)/(50010) 6.0010c m s m Hz νλ-==⨯⨯=⨯
1412(0.0024)(6.0010) 1.4410Hz ν∆=⨯=⨯
131/ 6.9410c t s ν-∆∆=⨯
8134(310/)(6.9410) 2.0810c c l c t m s s m --∆∆=⨯⨯=⨯
7. Solution:
)(2//0n n d s y -=∆αλ
8.Solution ：
λ=nd 2
m n
d 71084.12-⨯==
λ
9. Solution:
θαsin 2k a =，θβsin 2k b
=，mb a =，πβαm m 2==
N=number of fringes=m m a 2/2/==πππ
10. Solution:
sin m a m θλ=
sin /m m Y R θ
6(/)10,000/10/m Y m a R lines cm lines m λ=== So 610a m -=
761(589.5923)[1(5.89592310)/10](1.00)0.5895923Y nm m m m m
--=⨯=
'761(588.9953)[1(5.88955310)/10](1.00)0.5889953Y nm m m m m
--=⨯=
'411 5.9710Separation Y Y m -=-=⨯
11. Solution
sin /sin i t ti n θθ=; sin sin /sin(40)/1.5t i ti n θθ== ; 25.4t θ= .
2222tan ()/tan ()tan (14.6)/tan (65.4)0.014
i t i t R θθθθ=-+=-=
2222sin ()/sin ()sin (14.6)/sin (65.4)0.077i t i t R θθθθ⊥=-+=-=
1
()0.04552
R R R ⊥=
+= /()()/()67%p p n V I I I R R R R R ⊥⊥=+=+++=。