7.In a Young's double-slit experiment, a thin sheet of mica is placed over one of the two slits. As aresult, the center of the fringe pattern (on the screen) shifts by an amount corresponding to 30 dark bands. The wavelength of the light in this experiment is 480 mm and the index of the mica is 1.60.The mica thickness is:A) 0.090 mm B) 0.012 mm C) 0.014 mm D) 0.024 mm8. A diffraction pattern is produced on a viewing screen by illuminating a long narrow slit with lightof wavelength . If the slit width is decreased and no other changes are made:A) the intensity at the center of the pattern decreases and the pattern expands away from the bright centerB) the intensity at the center increases and the pattern contracts toward the bright centerC) the intensity at the center of the pattern does not change and the pattern expands away from the bright centerD) the intensity at the center of the pattern does not change and the pattern contracts toward the bright center9.Two stars that are close together are photographed through a telescope. The black and white film isequally sensitive to all colors. Which situation would result in the most clearly separated images of the stars?A)Small lens, red stars B) Large lens, blue starsC)Large lens, red stars D) Small lens, blue stars10.In a stack of three polarizing sheets the first and third are crossed while the middle one has its axisat 45°to the axes of the other two. The fraction of the intensity of an incident unpolarized beam of light that is transmitted by the stack is:A) 1/2 B) 1/3 C) 1/8 D) 1/4II. Filling in the blanks (Points: 3’×7)1. A simple harmonic oscillator consists of a mass m and anideal spring with spring constant k. Particle oscillates asshown in (i) with period T. If the spring is cut in half andused with the same particle, as shown in (ii), the springconstant is the period is2. A beam of x rays of wavelength 1x10-10m is found to diffractin second order from the face of a LiF crystal at a Bragg angleof 30°. The distance between adjacent crystal planes, in nm, isabout3. A standing wave pattern is established in a string as shown. Thewavelength of one of the component traveling waves is4.Two identical but separate strings, with the same tension, carrysinusoidal waves with the same amplitude. Wave A has afrequency that is twice that of wave B and transmits energy at a rate that is _____ that of wave B.5.Red light is viewed through a thin vertical soap film. At thesecond dark area shown, the thickness of the film, in terms of thewavelength within the film λ, is6. A diffraction grating just resolves the wavelengths 400.0 nm and400.1 nm in first order. The number of slits in the grating isIII. Calculating (49’)1. A wheel is free to rotate about its axel. A spring is attached to one of its spokes a distance rfrom the axel, as shown in the figure. Assuming that thewheel is a hoop of mass m and radius R, obtain thefrequency of a small oscillations of this system in terms ofm, R, r and the spring constant k. (12’)2. A string, tied to a sinusoidal vibrator at P and running over asupport at Q, is stretched by a block of mass m. Theseparation between P and Q is L. The amplitude of the motion at P is small enough for that point to be considered a node. (a) Determine the resonant frequency based on the wave speed v on the string and the length L of the string. (b) If L=1.2 m, the linear density of the string is 1.6g/m, and the frequency f of thevibrator is fixed at120Hz. what mass mallows the vibrator to setup the fourth harmonicon the string? (14)3.Monochromatic light of variable wavelength isincident normally on a thin sheet of plastic film inair. The reflected light is a minimum only forλ1=510nm and λ2=680nm in the visible spectrum.What is the thickness of the film? (n=1.58) (10)4.Light of wavelength 600 nm is incident normally on a diffraction grating. Two adjacent maximaoccur at angles given by sinθ=0.2 and sinθ=0.3. The fourth-order maxima are missing. (a) What is the separation between adjacent slits? (b) What is the smallest slit width this grating can have? (c) How many principle maxima are produced by the grating? (13)武汉理工大学试题标准答案及评分标准用纸 | 课程名称 大学物理AI. Selecting (only one correct answer in each of the problems. (3’×10)1.C ,2.B,3. B4.C5.D6.A ,7.D,8. A9.B, 10.CII. Filling in the blanks ( 3’×7 )1. 2. (0.2) 3. (4m) 4 (four times) 5 (3λ/4) 6(4000)III. Calculating (49’)1. (12) Ans: Solution: when the wheel rotates an angle θ from the equilibrium position, the spring force issin F kx kr θ=-=- (2)The torque acts on the wheel is:()()2cos sin cos sin cos F r Fr kr r kr ττθθθθθ=⨯⇒==-=- (2)When θ is very small 2kr I τθα≈-= (2)2I MR = (2)Thus the angular frequency is ω== (2)The frequency of the system is 2f ωπ== (2)2. (14)(a) Suppose we send a continuous sinusoidal wave along the string toward the right()1sin m y y kx t ωϕ=-+ (1)When the wave reaches the right end, it reflects and begins to travel back to left.()2sin m y y kx t ωϕπ=+++ (1)The principle of superposition gives, for the combined wave()22sin /2cos(/2)m y y kx t ϕπωπ=+++ (2) There is a node at position x=l, 2mvkl m f L π=⇒= (4)(b) For n = 4, v is the speed of the wavev mg τμμ= (2)()()2232/2120 1.2/4 1.6100.8469.8fl n m kg g μ-⨯⨯⨯===(4)3. Solution: because the reflect conditions from bottom surface and top surface are not same. Thus thepath-length difference is2/2nt δλ=+ (2)When the reflected light is a minimum, the path-length differenceis()()2/221/2/2nt m t m n λλλ+=+⇒= (2)n is the reflective index of the film. Because the reflected light isminimum only for λ1=510nm and λ2=680nm, we can get()()11221221/2/2//680/5104/3t m n m n m m λλλλ==⇒=== (2)And m 1, m 2 must satisfy the condition 121m m =+, thus m 1=4, m 2=3. (2)The thickness of the film is ()11/24510/(2 1.58)646t m n nm nm λ==⨯⨯= (2)4. (a) The location of maxima can be determined by equation of grating.sin d m θλ= (2)λ is the wavelength, and m is an integer. Let m be the order number for the line with sin θ = 0.2 and m +1 be the order number for the line with sin θ = 0.3.thus the separation of between adjacent slits can be solved out()60.30.210610d d m λλ--=⇒==⨯ (3)(b) Minima of the single-slit diffraction pattern occur at angles θ given bya sin θ = k λ, (2)Where a is the slit width. Since the fourth-order interference maximum is missing, it must fall at one of these angles.6sin 1.5104m d d a m d a m λλθ-==⇒===⨯ (3)。
