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Light of wavelength 632.8 nm illuminates a single slit, and a diffraction pattern is formed on a screen 1.00 m from the slit. (a) Using the data in the following table, plot relative intensity versus position. Choose an appropriate value for the slit width a and, on the same graph used for the experimental data, plot the theoretical expression for the relative intensity
where ϕ = (πa sin θ)/λ. (b) What value of a gives the best fit of theory and experiment?
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Chapter 38 Solutions
Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)
- Consider a single-slit diffraction pattern for =589 nm, projected on a screen that is 1.00 m from a slit of width 0.25 mm. How far from the center of the pattern are the centers of the first and second dark fringes?arrow_forwardTwo slits of width 2 m, each in an opaque material, are separated by a center-to-center distance of 6 m. A monochromatic light of wavelength 450 nm is incident on the double-slit. One finds a combined interference and diffraction pattern on the screen. (a) How many peaks of the interference will be observed in the central maximum of the diffraction pattern? (b) How many peaks of the interference will be observed if the slit width is doubled while keeping the distance between the slits same? (c) How many peaks of interference will be observed if the slits are separated by twice the distance, that is, 12 m, while keeping the widths of the slits same? (d) What will happen in (a) if instead of 450-nm light another light of wavelength 680 nm is used? (e) What is the value of the ratio of the intensity of the central peak to the intensity of the next bright peak in (a)? (f) Does this ratio depend on the wavelength of the light? (g) Does this ratio depend on the width or separation of the slits?arrow_forwardProblem 2: Consider light that has its third minimum at an angle of 23.6° when it falls on a single slit of width 3.55 μm. Randomized Variables 9 = 23.6° w = 3.55 um D Find the wavelength of the light in nanometers. λ=1 sin() cos() cotan() asin() atan() acotan() tanh() cosh() O Degrees Hints: 2% deduction per hint. Hints remaining: 2 Submit tan() JU acos() E sinh() cotanh() Radians Hint ( + 7 8 9 4 5 6 1 0 VO BACKSPACE Feedback 2 3 All content © 2022 Expert TA, LLC DEL HOME END I give up! Feedback: 2% deduction per feedback. CLEARarrow_forward
- In an interference experiment using a monochromatic source emitting light of wavelength å, the fringes are produced by two long, narrow slits separated by a distance d. The fringes are formed on a screen which is situated at a distance D >> d. Write down an expression for the fringe width w. Please use Il * II for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate. Use "lambda" (without the quotes) for å in the equation box. For example, use d*lambda for d2. Please use the "Display response" button to check you entered the answer you expect.arrow_forwardProblem 18: Consider a single slit that produces its first minimum at 54° for 590 nm light. Randomized Variablesθ1 = 54 °θ1 = 54 °θ2 = 67 °λ1 = 590 nm Part (a) What is the width of the single slit, w, in nanometers?Numeric : A numeric value is expected and not an expression.w = __________________________________________ Part (b) Find the wavelength, in nanometers, of light that has its first minimum at 67°.Numeric : A numeric value is expected and not an expression.λ2 = __________________________________________arrow_forwardA laser beam is normally incident on a single slit with width 0.580 mm. A diffraction pattern forms on a screen a distance 1.20 m beyond the slit. The distance between the positions of zero intensity on both sides of the central maximum is 2.12 mm. Calculate the wavelength of the light (in nm). X Find the relationship among y, the distance from the central maximum to the first minimum, L, and 0, and then apply the equation for the Fraunhofer diffraction pattern. Solve for A. Hint: use a small-angle approximation. nmarrow_forward
- Problem 20: Consider 642 nm light falling on a single slit of width 19.5 μm.Randomized Variablesλ = 642 nmw = 19.5 μm Part (a) Find the angle, in degrees, of the third diffraction minimum for the light.Numeric : A numeric value is expected and not an expression.θ3 = __________________________________________Part (b) What slit width (in micrometers) would place this minimum at 85.0°?Numeric : A numeric value is expected and not an expression.w' = __________________________________________arrow_forwardMonochromatic light of wavelength 612 nm falls on a slit. If the angle between the first two bright fringes on either side of the central maximum is 34°, estimate the slit width. Express your answer to two significant figures and include the appropriate units. Di D= 6 μ μA Ω % μm ?arrow_forwardIn the two-slit interference experiment, the slit widths are each 4.0 μm, their separation is 24.0 μm, the wavelength is 600 nm, and the viewing screen is at a distance of 2.00 m from the slits. Point P lies at distance y =5.0 cm from the center of the pattern. (a) Without diffraction effects taken into account, what is the ratio of IP to the intensity Im at the center of the pattern? (b) With diffraction effects taken into account, what is the ratio of IP to the intensity Im at the center of the pattern?arrow_forward
- two radiofrequency point sources S1 and S2, separated by distance d= 2.0 m, are radiating in phase with l = 0.50 m. A detector moves in a large circular path around the two sources in a plane containing them. How many maxima does it detect?arrow_forwardThe limit to the eye’s acuity is actually related to diffraction by the pupil. What is the angle between two just-resolvable points of light for a 3.00-mm-diameter pupil, assuming an average wavelength of 550 nm?arrow_forwardIn a double slit interference pattern, the intensity at the peak of the central maximum(m = 0) is I0.(a) Calculate the intensity you measure at a point P in the pattern where the phasedifference between the waves from slits S1 and S2 is 45.0◦.(b) Calculate the difference in path at point P if the frequency of the light used inthe experiment is ν = 600 THz An object is 2.00-cm-tall and is positioned 75.0 cm to the left of lens 1. Lens 1 isa converging lens with focal length f1 = 35.0 cm. A second converging lens, lens 2,having a focal length f2 = 50.0 cm, is located 200.0 cm to the right of lens 1, along thesame optic axis, and will have the image produced by lens 1 (I1) as its object.(a) Find the location (s01) and size (y01) of the image formed by lens 1. (b) Find the location (s02) and size (y02) of the image formed by lens 2.arrow_forward
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