describe the meaning of wavelength/n the original phases (Ø, and ø, ) for the two sources are the same, Aø= 2nnd sin 035B – Experiment: Two Slit InterferenceEquipment: Pasco magnetic optical rail; Red semiconductor laser diode; diode powersupply; Pasco Multiple Slit mask; a white screen to view the interference pattern; a smallruler to measure distance on the interference image.Background: If waves with the same wavelength emanate from two points and travel in straight paths (riand r2) through a uniform material (index n) to a common point as shown to the right, they will be out ofphase according to:2rn(, -r,)Ag =+( - 42). If ri and r2 are very large compared to the distance between the sources d,then (r - r,)=d sin 0 where 0 is the angle between the normal to a line from one source to the other anda line from sources to measurement point. This is shown schematically in the lower sketch above. If alsowhich exhibits a2,maximum in intensity whenever Aø is an integer (m) multiple of 2x , or when må, = nd sin 0m -Тоp ViewScreenTydDD » d1) We made a point of labeling the wavelength with a subscript v.a) What do you think 2 with this subscript denotes?b) Describe the meaning of ^ 35D – The Diffraction GratingObjective: Determine the spacing between lines of a diffraction grating by observing interference peaksfor light of a specific wavelength.Equipment: Low power laser. Diffraction grating, PASCO magnetic optics rail, PASCOmagnetic optics carrier, Black metal safety screen, Ruler.LASER SAFETY; Avoid shining the laser in these laboratories directly intoanyone'seyes. Prolonged direct viewing of the beam can lead to permanent eye damage.Background: A diffraction grating consists of a reflective or transmitting surface with a periodicarray of lines. In the simplest theoretical model, we assume that each line on the grating acts as ainfinitesimally thin emission source with all of the sources emitting at the same wavelength andin set phase to one another. For a beam of wavelength A at normal incidence to the plane of themåwhere m is an integerdgrating, interference peaks will be observed at angles 0 = arcsin- (Order of Interference) and d is the distance between the grating emitting lines.Screeny-ま -y+Diffraction GratingLaser ApparatusD Distance to ScreenProcedure: Set up the laser so that it shines through the middle of a grating held in place on a magneticcarrier. Measure the lateral displacement between the central maximum peak and the two interferencemaxima on either side of it. Record this measurement and the distance D of the ruler from the grating tothe screen to compute the angle. (The angle may be large – greater than 20 degrees – therefore theviewing ruler may have to be close to the grating.)Make at least 4 measurements with different D's. Use a laser wavelength 2= 650 nm and compute thed-spacing for each measurement.TRIALSD (mm)y+y-0+0-d+d-19585775217775220 18534Average d-spacing =Gratings are often described in terms of the number of lines per centimeter n.Convert your d-spacing into lines per centimeter.+/-(from standard deviation of your 8 measurements ±d.

Two slit interference experiment is given.

35B – Experiment: Two Slit Interference Equipment: Pasco magnetic optical rail; Red semiconductor laser diode; diode power supply; Pasco Multiple Slit mask; a white screen to view the interference pattern; a small ruler to measure distance on the interference image. Background: If waves with the same wavelength emanate from two points and travel in straight paths (ri and r2) through a uniform material (index n) to a common point as shown to the right, they will be out of phase according to: 2an(r-r). Aø =- +( – 42) . If rị and r2 are very large compared to the distance between the sources d, then (r -r,)Ed sin 0 where 0 is the angle between the normal to a line from one source to the other and a line from sources to measurement point. This is shown schematically in the lower sketch above. If also the original phases (, and 6, ) for the two sources are the same, Aø=: 2rnd sin e which exhibits a maximum in intensity whenever Aø is an integer (m) multiple of 27 , or when m2, = nd sin 0 . Top View Screen d. D D » d 1) We made a point of labeling the wavelength with a subscript v. a) What do you think 2 with this subscript denotes? b) Describe the meaning of

35B – Experiment: Two Slit Interference Equipment: Pasco magnetic optical rail; Red semiconductor laser diode; diode power supply; Pasco Multiple Slit mask; a white screen to view the interference pattern; a small ruler to measure distance on the interference image. Background: If waves with the same wavelength emanate from two points and travel in straight paths (ri and r2) through a uniform material (index n) to a common point as shown to the right, they will be out of phase according to: 2an(r-r). Aø =- +( – 42) . If rị and r2 are very large compared to the distance between the sources d, then (r -r,)Ed sin 0 where 0 is the angle between the normal to a line from one source to the other and a line from sources to measurement point. This is shown schematically in the lower sketch above. If also the original phases (, and 6, ) for the two sources are the same, Aø=: 2rnd sin e which exhibits a maximum in intensity whenever Aø is an integer (m) multiple of 27 , or when m2, = nd sin 0 . Top View Screen d. D D » d 1) We made a point of labeling the wavelength with a subscript v. a) What do you think 2 with this subscript denotes? b) Describe the meaning of

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter27: Wave Optics

Section: Chapter Questions

Problem 4OQ

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Similar questions

Consider the single-slit diffraction pattern for =600 nm, D=0.025 mm , and x=2.0 m. Find the intensity in terms of Io at =0.5 , 1.0°, 1.5°, 3.0°, and 10.0°.
What is the angular width of the central fringe of the interference pattern of (a) 20 slits separated by d=2.0103 mm? (b) 50 slits with the same separation? Assume that =600 nm.
Two slits each of width 1800 nm and separated by the center-to-center distance of 1200 nm are illuminated by plane waves from a krypton ion laser-emitting at wavelength 461.9 nm. Find the number of interference peaks in the central diffraction peak.
A hydrogen gas discharge lamp emits visible light at four wavelengths, =410 , 434, 486, and 656 nm. (a) If light from this lamp falls on a N slits separated by 0.025 mm, how far from the central maximum are the third maxima when viewed on a screen 2.0 m from the slits? (b) By what distance are the second and third maxima separated for l=486 nm?
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?
A monochromatic light of wavelength 589 nm incident on a double slit with slit width 2.5 m and unknown separation results in a diffraction pattern containing nine interference peaks inside the central maximum. Find the separation of the slits.
Light from a helium-neon laser ( = 632.8 nm) is incident on a single slit. What is the maximum width of the slit for which no diffraction minima are observed?
When a monochromatic light of wavelength 430 nm incident on a double slit of slit separation 5 m, there are 11 interference fringes in its central maximum. How many interference fringes will be in the central maximum of a light of wavelength 632.8 nm for the same double slit?
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?
Coherent light rays of wavelength strike a pair of slits separated by distance d at an angle 1, with respect to the normal to the plane containing the slits as shown in Figure P27.14. The rays leaving the slits make an angle 2 with respect to the normal, and an interference maximum is formed by those rays on a screen that is a great distance from the slits. Show that the angle 2 is given by 2=sin1(sin1md) where m is an integer.
In Figure P27.7 (not to scale), let L = 1.20 m and d = 0.120 mm and assume the slit system is illuminated with monochromatic 500-nm light. Calculate the phase difference between the two wave fronts arriving at P when (a) = 0.500 and (b) y = 5.00 mm. (c) What is the value of for which the phase difference is 0.333 rad? (d) What is the value of for which the path difference is /4?
A 5.08-cm-long rectangular glass chamber is inserted into one arm of a Michelson interferometer using a 633-nm light source. This chamber is initially filled with air (n=1.000293) at standard atmospheric pressure but the air is gradually pumped out using a vacuum pump until a near perfect vacuum is achieved. How many fringes are observed moving by during the transition?