Part A (Figure 1) shows the fringes observed in a double-slit interference experiment when the two slits are illuminated by white light. The central maximum is white because all of the colors overlap. This is not true for the other fringes. The m = 1 fringe clearly shows bands of color, with red appearing farther from the center of the pattern, and blue If the slits that create this pattern are 25 µm apart and are located 0.85 m from the screen, what are the m = 1 distances from the central maximum for red (700 nm) and violet (400 nm) light? closer. Express your answers in centimeters. Enter your answers separated by a comma. ? Y1 red,Y1 violet = cm

Part A (Figure 1) shows the fringes observed in a double-slit interference experiment when the two slits are illuminated by white light. The central maximum is white because all of the colors overlap. This is not true for the other fringes. The m = 1 fringe clearly shows bands of color, with red appearing farther from the center of the pattern, and blue If the slits that create this pattern are 25 µm apart and are located 0.85 m from the screen, what are the m = 1 distances from the central maximum for red (700 nm) and violet (400 nm) light? closer. Express your answers in centimeters. Enter your answers separated by a comma. ? Y1 red,Y1 violet = cm

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter4: Diffraction

Section: Chapter Questions

Problem 34P: Two slits of width 2 m, each in an opaque material, are separated by a center-to-center distance of...

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Fig. 3 shows three situations of the same light of wavelength λ = 670 nm, falling on a slit at 2.58 m from the screen.slit 2.58 m away from the screen. The unit of the position axis is centimeter.(a) Do the figures deal with a single slit or a double slit? Explain.(b) Considering your answer in (a) estimate, for each case, the slit opening (a) if the problemsingle slit and the slit opening and separation of the slits (a and d) if the problem is a double slit.crack. Justify all the logic and steps used.
An intereference pattern is produced by light with a wavelength of 560 nm from a distant source incident on two identical parallel slits seperated by a distance (between centers) of 0.580 mm. (A) if the slits are very narrow what would be the angular position of the first order two slit intereference maxima? Express your answer in radians. (B) what would be the angular position of the second order two slit intereference maxima in this case? (C) let the slits have a width of 0.330 mm. In terms of the intensity at the center of the central maximum what is the intensity at the angular position of theta? (D) what is the intensity at the angular position of theta2?
Consider a single slit being illuminated by light with wavelength λ. Part (a) What is the minimum width, w1min, expressed as a multiple of λ, for which the slit produces the first minimum? Part (b) What is its minimum width of the slit, w50,min, if it produces 50 minima? Again, express this in multiples of λ. Part (c) What if it produces 1000 minima?
Consider a single slit that produces its first minimum for 630 nm light at an angle of 26 degrees Part a: How wide is the single slit in meters? Part b: at what angle ( in degrees) will the second be minimum
How much diffraction spreading does a light beam undergo? One quantitative answer is the full width at half maximum of the central maximum of the single-slit Fraunhofer diffraction pattern. You can evaluate this angle of spreading in this problem. (a) as shown, define φ = πa sin φ/λ and show that at the point where I = 0.5Imax we must have φ = √2 sin φ. (b) Let y1 = sin φ and y2 = φ = /√2. Plot y1 and y2 on the same set of axes over a range from φ = 1 rad to φ = π/2 rad. Determine φ from the point of intersection of the two curves. (c) Then show that if the fraction λ/a is notlarge, the angular full width at half maximum of the central diffraction maximum is θ = 0.885λ/a. (d) What If? Another method to solve the transcendental equation φ = √2 sin φ in part (a) is to guess a first value of φ, use a computer or calculator to see how nearly it fits, and continue to update your estimate until the equation balances. How many steps(iterations) does this process take?
Monochromatic light of wavelength 530 nm passes through a horizontal single slit of width 1.5 m in an opaque plate. A screen of dimensions 2.0m2.0m is 1.2 m away from the slit. (a) Which way is the diffraction pattern spread out on the screen? (b) What are the angles of the minima with respect to the center? (c) What are the angles of the maxima? (d) How wide is the central bright fringe on the screen? (e) How wide is the next bright fringe on the screen?
Ten narrow slits are equally spaced 0.25 mm apart and illuminated with yellow light of wavelength 580 nm. (a) What are the angular positions of the third and fourth principal maxima? (b) What is the separation of these maxima on a screen 2.0 m from the slits?
A diffraction grating with 2000 lines per centimeter is used to measure the wavelengths emitted by a hydrogen gas discharge tube. (a) At what angles will you find the maxima of the two first-order blue lines of wavelengths 410 and 434 nm? (b) The maxima of two other first-order lines are found at 1=0.097 rad and 2=0.132 rad . What are the wavelengths of these lines?
(a) By differentiating Equation 4.4, show that the higher-order maxima of the single-slit diffraction pattern occur at values of that satisfy tan= . (b) Plot y=tan and y= versus and find the intersections of these two curves. What information do they give you about the locations of the maxima? (c) Convince yourself that these points do not appear exactly =(n+12) , where n=0,1,2,, but are quite close to these values. I=I0( sin)2 (4.4)
Two 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?
(a) What is the smallest separation between two slits that will produce a second-order maximum for any visible light? (b) For all visible light?
A Two slits are separated by distance d and each has width w. If d = 2w, how many bright fringes are within the central maximum of the diffraction pattern?