Physics 72: Chapter 35 and 36 Problem Set Name: Lecturer: Mr Carlos Baldo III
Summer 2010 Score: Section: X7-7
Encircle the letter of the correct answer. Solve each problem clearly and completely for full credit. 1.
So intense. What is the intensity of light at any point in the interference pattern due to two identical sources (each with intensity I0), if the phase difference of the two sources is 60°? A. Zero B. 0.25I0 C. 0.75I0 D. I0 E. 3I0
2.
Fringe A. B. C. D. E.
3.
Wedge-shaped gap interference. What happens to the fringe spacing as θ is increased? (For small angles, tanθ ≈θ)? A. no change B. increases C. decreases D. it depends on the thickness of both glasses E. it depends on the thickness of the top glass
4.
Constructive interference. Two coherent light sources with wavelength λ and located at points A and B interfere constructively at a point P. Which of the following statements is definitely TRUE? I. Point P is very far from both points A and B. II. The distance of each source to point P is an integral multiple of λ III. The difference in the distances of each source to point P is an integral multiple of λ A. B. C. D. E.
names. Which of the following statements about two-slit interference fringes is TRUE? The first-order minimum has m = 1.5 There are two second-order maxima. The first-order maximum is at the center of the fringe pattern. The second-order minimum is between the second- and third-order maxima. The central maximum is also known as the first-order maximum.
I only II only III only I and II I and III
5.
Young's experiment. A laser beam with wavelength 250 nm is incident on two slits and produces an interference pattern on a screen 1.2 m away from the slits. The fourth-order maximum is located 2 cm from the central maximum. What is the separation distance of the slits? A. 120 µm B. 60 µm C. 30 µm D. 20 µm E. 10 µm
6.
Fringe energy. Young's experiment was performed on two setups that differ only in their slit separation distances. The distance between fringes in the first setup is twice than the second setup. What can be said about the net energy of the fringes? A. The net energy of the fringes in the first setup is equal to the net energy in the second setup B. The net energy of the fringes in the first setup is twice than the net energy in the second setup C. The net energy of the fringes in the first setup is four times the net energy in the second setup D. The net energy of the fringes in the second setup is twice than the net energy in the first setup E. The net energy of the fringes in the second setup is four times the net energy in the second setup
Physics 72: Chapter 35 and 36 Problem Set
Summer 2010
7.
Colored bands. Different colored bands/fringes are observed in a soap film suspended in a loop of wire that is held in air. What color is seen when the soap film is 175 nm thick? A. Indigo (λ = 437.5 nm) B. Green (λ = 525 nm) C. Orange (λ = 612.5 nm) D. Red (λ = 700 nm) E. Black
8.
Liquid gap interference. A wedge-shaped film of air is made by placing a small slip of paper between the edges of two flat pieces of glass as shown in the figure. Light of wavelength 250 nm is incident normally on the top glass and the angle made by the plates is θ=3 × 10-4 rad. If the gap between the plates is filled by liquid having a refractive index equal to that of glass, how many interference fringes per centimeter are observed? A. 24 fringes per centimeter B. 12 fringes per centimeter C. 6 fringes per centimeter D. 3 fringes per centimeter E. No interference fringes are observed
For the next two numbers, consider two slits illuminated by a coherent light source. The wavelength of the light, slit separation and slit width are made such that the interference pattern shown at the right is seen at a distant screen. 9.
Gummy film 1. A gummy film is placed behind one of the slits, causing a 180° phase shift for the light through this slit. How will the resulting interference pattern look like?
10. Gummy film 2. The gummy film is then removed. If the distance between the slits is decreased to 1/2 of its original value, how would the interference pattern look like?
11. Newton's Rings. A Newton's-ring apparatus consists of a glass lens with radius of curvature R that rests on a flat glass plate. The thin film is air of variable thickness. The pattern is viewed by reflected light of wavelength λ. For a thickness t, the condition for a bright interference ring is given by what equation? Let m = 0, 1, 2, … A. t = mλ B. t = mλ/2 C. t = mλ/4 D. t = (m + ½) λ/2 E. t = (m + ½) λ 12. Soap film. What is the thinnest soap film (excluding the case of zero thickness) that appears black when illuminated with light with wavelength 266nm? The index of refraction of the film is 1.33 and there is air on both sides of the film. A. 1000 nm B. 800 nm C. 100 nm D. 200 nm E. 400 nm
Physics 72: Chapter 35 and 36 Problem Set
Summer 2010
13. Interference Fringes. The observed interference fringes on three Young's experiment setups are shown below. The setups differ only in the incident light. How are the incident frequencies related?
N A. B. C. D. E.
I
P
fP < fI < fN fN < fI < fP fN < fP < fI fI < fN < fP fI < fP < fN
14. Diffraction. Which of the following is/are TRUE regarding the single slit diffraction pattern? I. One bright band is visible II. Multiple bright bands of equal brightness are visible III. Multiple bright bands of varying brightness are visible A. B. C. D. E.
I only II only III only I and III I and II
15. Dark fringe. A diffraction pattern was formed by a single slit. The central bright maximum has a width of 6 mm. What is the position of the third dark fringe is as measured from the center? A. 3 mm B. 6 mm C. 9 mm D. 12 mm E. 15 mm 16. Width. The same single slit diffraction setup is used on separate trials with three different light wavelengths (λ1=400 nm, λ2=550 nm, λ3=700 nm). Arrange the three in order of increasing width of the central bright fringe. A. λ1 < λ3 < λ2 B. λ1 < λ2 < λ3 C. λ2 < λ1 < λ3 D. λ3 < λ1 < λ2 E. λ3 < λ2 < λ1 17. Central fringe. Light of wavelength λ=700 nm is used in a single slit diffraction setup with three slit width settings (a1=0.1 µm, a2=10 µm, a3=100 µm). Arrange the three in order of increasing width of the central bright fringe. A. a1 < a3 < a2 B. a1 < a2 < a3 C. a2 < a1 < a3 D. a3 < a1 < a2 E. a3 < a2 < a1 18. Variable slit. Light of wavelength λ=500nm is used in a single slit diffraction setup with three variable slit–screen distances (x1=1 m, x2=10 m, x3=100 m). Arrange the three in order of increasing width of the central bright fringe. A. x1 < x3 < x2 B. x1 < x2 < x3 C. x2 < x1 < x3 D. x3 < x1 < x2 E. x3 < x2 < x1 19. Diffraction 1. Which among the colors of the visible light will yield the least width of the bright central maximum after passing through a single slit?
Physics 72: Chapter 35 and 36 Problem Set A. B. C. D. E.
Summer 2010
Red Yellow Green Violet Each will produce equal width of central maximum
20. Central brightness. The same single slit diffraction setup is used on separate trials with light of three different wavelengths (λ1=400 nm, λ2=550 nm, λ3 = 700 nm), all having the same initial intensity. Arrange the three in order of increasing brightness in the middle of the central maximum. A. λ1 = λ3 = λ2 B. λ1 < λ2 < λ3 C. λ2 = λ1 < λ3 D. λ3 = λ1 < λ2 E. λ3 < λ2 < λ1 21. Two slit. In a two–slit diffraction experiment in which each slit has width a and separated by a distance d=3a, how many bright fringes can be counted inside the original diffraction central maximum? A. 7 B. 6 C. 3 D. 4 E. 5 For the next two numbers, green light of wavelength λ=560 nm is used in three diffraction experiments with varying number of slits (N1=3, N2=5, N3=7). Each slit is very narrow, and any two adjacent slits are separated by the same distance d. 22. Principal 1. Arrange the slit numbers in order of increasing width of the principal maxima. A. N1 = N2 = N3 B. N1 < N2 < N3 C. N1 = N2 < N3 D. N3 = N1 < N2 E. N3 < N2 < N1 23. Principal 2. Arrange the slit numbers in order of increasing brightness of the principal maxima. A. N1 = N2 = N3 B. N1 < N2 < N3 C. N1 = N2 < N3 D. N3 = N1 < N2 E. N3 < N2 < N1 For the next two numbers, consider the interference pattern. 24. Slits. How many slits produced the above pattern? A. 5 B. 6 C. 7 D. 8 E. 9 25. Principal maxima. What happens to the distance between principal maxima if the slit widths of the slits are equally doubled? A. Increases by a factor of 4 B. Increases by a factor of 2 C. Decreases by a factor of 4 D. Decreases by a factor of 2 E.
Remains the same
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