Concept explainers
Slit 1 of a double-slit is wider than slit 2 so that the light from slit 1 has an amplitude exactly 3 times that of the light from slit 2. Show that Equation 36.9 is replaced by the following equation for this situation:
Begin by assuming that the total magnitude of the electric field at point P on the screen in Figure 36.4 is the superposition of two waves, with electric field magnitudes
The phase angle ϕ in E2 is due to the extra path length traveled by the lower beam in Figure 36.4. You will need to evaluate the integral of the square of the sine function over one period. Refer to Figure 32.5 for an easy way to perform this evaluation. You might find the following trigonometric identities helpful:
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Chapter 36 Solutions
Physics:f/sci.+engrs.,ap Ed.
- In experiments with his interferometer, Michelson found that the red cadmium line at λ=643.8nm produced fringes until one of the arms of the interferometer was moved 25cm from initially being at the coincidence or equal path length position. a. How many fringes moved through the field of view? b. What is the approximate coherence time of the light?arrow_forwardIn a double-slit interference experiment, d is the distance between the centers of the slits and w is the width of each slit, as shown in the figure above. For incident plane waves, if an interference maximum on a distant screen will fall at a diffractive minimum, which of the following relations between d and w is correct? @ 3d=2w @ 2d=3w. @d=3¹/2w. @d=2¹/2w @ 2d=w.arrow_forwardWrite down an expression for the width of the central bright line on a screen in the single slit diffraction experiment in terms of the diffraction slit (without the quotes) for products (e.g. width d, the distance from the slit to the screen D and the wavelength of light A. Consider D>> d. Please use "*" B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate. For exponents (e.g. A²) use A*A or A^2 notation: thus A³/B should appear as either A*A*A/B or A^3/B. For greek letters use "theta" (without the quotes) and for trigonometric functions use "cos", "tan", "sin" (without the quotes). Thus for Acose use A* cos theta. Please use the "Display response" button to check you entered the answer you expect. Answer: Display responsearrow_forward
- Figure 1 shows the viewing screen in a double-slit experiment with monochromatic light. Fringe C is the central maximum. The fringe separation is Δy Suppose the wavelength of the light is 430 nm . How much farther is it from the dot on the screen in the center of fringe E to the left slit than it is from the dot to the right slit?arrow_forwardConsider a variety of colors of visible light (say 400 nm to 700 nm) falling onto a pair of slits. a) What is the smallest separation (in nanometers) between two slits that will produce a second-order maximum for some visible light? b) What is the smallest separation (in nanometers) between two slits that will produce a second-order maximum for all visible light?arrow_forwardThe ship in the figure below travels along a straight line parallel to the shore and a distance d = 710 m from it. The ship's radio receives simultaneous signals of the same frequency from antennas A and B, separated by a distance L = 750 m. The signals interfere constructively at point C, which is equidistant from A and B. The signal goes through the first minimum at point D, which is directly outward from the shore from point B. Determine the wavelength of the radio waves.arrow_forward
- The light intensity vs. position graph of a double-slit experiment is shown below. The graph was made with helium-neon laser light of wavelength 630 nm shined through two very narrow slits separated by a small distance. The slits were 2.0 meters away from the probe. What is the path-length difference (from the two slits to the screen) when the probe is at position 9.0 mm, in nm? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement. Lasilian Position of probe (mm) Light levelarrow_forwardX rays of wavelength 0.0820 nm are scattered from the atoms of a crystal. The second-order maximum in the Bragg reflection occurs when the angle is 20.5°. (Figure 1) For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of X-ray diffraction. Part A What is the spacing between adjacent atomic planes in the crystal? Express your answer in nanometers. ΓΙ ΑΣΦ d = Submit Previous Answers Request Answer ? nmarrow_forwardIn a Young's double-slit experiment, a set of parallel slits with a separation of 0.130 mm is illuminated by light having a wavelength of 550 nm and the interference pattern observed on a screen 3.50 m from the slits. (a) What is the difference in path lengths from the two slits to the location of a fifth order bright fringe on the screen? 1.1 Your response differs from the correct answer by more than 10%. Double check your calculations. um (b) What is the difference in path lengths from the two slits to the location of the fifth dark fringe on the screen, away from the center of the pattern? X umarrow_forward
- Q. A grating having 5000 lines per cm is used under normal incidence of light. What will happen to the observed spectrum if 90% of the ruled width of the grating is covered? Please solve this, urgently. Thankyou!!!arrow_forwardA beam of monochromatic light is incident on a single slit of width 0.630 mm. A diffraction pattern forms on a wall 1.35 m beyond the slit. The distance between the positions of zero intensity on both sides of the central maximum is 2.10 mm. Calculate the wavelength of the light. .049 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. nmarrow_forwardYou shine light with an unknown wavelength through two slits that are an unknown distance, d, apart. You put the screen a distance, D = 41 cm, behind the slit plate, and find that the width of the central maximum is Ayo = 1.43 cm. Use the small-angle approximation to obtain the symbolic expressions. (a) Write symbolic expressions for each of the following in terms of 2, d, D (and integers) as needed. 01min = y1min Ayo = (b) Write a symbolic expression for the ratio of 2/d, in terms of the given variables, Ayo, and D, then calculate its numeric value.arrow_forward
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