To understand the derivations of, and be able to use, the equations for Fraunhofer diffraction.
Diffraction is a general term for interference effects related to edges or apertures. Diffraction is more familiar in waves with longer wavlengths than those of light. For example, diffraction is what causes sound to bend around corners or spread as it passes through a doorway. Water waves spread as they pass between rocks near a rugged coast because of diffraction. Two different regimes for diffraction are usually identified: Fresnel and Fraunhofer.
Fresnel diffraction is the regime in which the diffracted waves are observed close (as compared to the size of the object causing the diffraction) to the place where they are diffracted. Fresnel diffraction is usually very complicated to work with. The other regime, Fraunhofer diffraction, is much easier to deal with. Fraunhofer diffraction applies to situations in which the diffracted waves are observed far from the point of diffraction. This allows a number of simplifying approximations to be used, reducing diffraction to a very manageable problem.
An important case of Fraunhofer diffraction is the pattern formed by light shining through a thin slit onto a distant screen (see the figure). (Figure 1)
Notice that if the light from the top of the slit and the light from the bottom of the slit arrive at a point P on the distant screen with a phase difference of 2π, then the electric field vectors E⃗ of the light from each part of the slit will cancel completely, resulting in a dark fringe. To understand this phenomenon, picture a phasor diagram for this scenerio (as show in the figure).
A phasor diagram consists of vectors (phasors) with magnitude proportional to the magnitude of the electric field of light from a certain point in the slit. The angle of each vector is equal to the phase of the light from that point. These vectors are added together, and the resultant vector gives the net electric field due to light from all points in the slit. In the situation described above, since the magnitude of the electric field vectors is the same for light from any part of the slit and the angle of the phasors changes continuously from 0 to 2π, the phasors will make a complete circle, starting and ending at the origin. The distance from the origin to the endpoint of the phasor path (also the origin) is zero, and so the magnitude of the electric field at point P is zero.
you are getting incorrect response probably because you used a instead of b
To understand the derivations of, and be able to use, the equations for Fraunhofer diffraction. Diffraction...
In the double-slit experiment of the figure, the electric fields of the waves arriving at point Pare given by Ep ( 2.34 μ /m) sin(( 2.25x 1015)t] E2 ( 2.34 V/m) sin[( 2.25 x 1015)t + 39.6 rad], where time t is in seconds. (a) What is the amplitude of the resultant electric field at point P? (b) What is the ratio of the intensity Ip at point P to the intensity Icen at the center of the interference pattern?...
fill in the table. answer the questions. IDK the measured values. You have to figure it out thru a simulation. Part 2. Single Slit Diffraction 1 T 1 DT SINGLE SLIT L If the viewing screen is far away, the rays heading for any point on the screen are essentially parallel. Consider the waves emanating from the upper half and lower half of the slit. Destructive interference, a dark fringe, occurs if the path difference from any point in the...
Please answer #9 below and show all work. Will thumbs up for a prompt response (within 1 hour), thanks! QAR Ay-Ay E -100 Repeat the process to determine the width of the central peak for the remaining cases. sy Slit width Yminl min2 Ay=min2-min) Theoretical Ay Percent difference 0.02mm 2.20 mm 20.30 mm 25.3mm 4.98 0.04 mm 7.10mm 19.00mm 11.9mm 12.7mm 6.56 0.08 mm 19.75mm 15.80mm 6.05mm 6.33mm 4.56 0.16mm 11.05mm 14.15mm 3.100mm 3.17mm 2.2% 24.1mm 9. Use Equation (4)...
Please help me out with these questions Problem 2 Part A Maxwell's equations can be used to show that electromagnetic waves can propagate through space. (a) Describe the key aspects of an electromagnetic wave. Your description should mention the electric and magnetic fields, direction of propagation, and speed. A diagram would be useful in explaining these concepts (b) At some point in space, a sinusoidal electromagnetic wave has an intensity of 2.5 Wm-2 Calculate the amplitudes of the electric field...
As shown in the figure, a proton is at the origin and an unknown charge is at x = +4.0 nm. If the net electric force on a small positive test charge is zero at x = -3 nm, what is the magnitude and sign of the unknown charge? test charge q unknown charge Q proton x=-3 nm x=0 x=+4 nm 0 +0.19e 0 -0.19e 0 +5.4e 0 -5.4e 0 -2.7e The figure shows two electrons separated by a distant...
Maxwell's equations can be used to show that electromagnetic waves can propagate through space (a) Describe the key aspects of an electromagnetic wave. Your description should mention the electric and magnetic fields, direction of propagation, and speed. A diagram would be useful in explaining these concepts (b) At some point in space, a sinusoidal electromagnetic wave has an intensity of 2.5 Wm2 Calculate the amplitudes of the electric field and the magnetic field at this point. Ensure that you include...
please answer all questions Question 1 5 pts As shown in the figure, an unknown charge is located at the origin and an electron is located at x = +0.2 nm. If the net electric force on a small positive test charge is zero at x = -1.5 nm, what is the magnitude and sign of the unknown charge? unknown charge test charge q electron e X=-1.5 nm x=0 x=+0.2 nm 0 -0.78e 0 +0.78e 0 -0.018e +0.018e +28e The...
A large, flat sheet carries a uniformly distributed electric current with current per unit widthJs. This current creates a magnetic field on both sides of the sheet, parallel to the sheet and perpendicular to the current, with magnitude B- 0's. If the current is in the y direction and oscillates in time according to 2 /max (cos ωガーJmax[cos (-wtjj the sheet radiates an electromagnetic wave. The figure below shows such a wave emitted from one point on the sheet chosen...
can help solving question 28a-d? Do we use E=cB or dE/dt = - dB/dt for question a? waves of Ireny means of communication? 34. 28. A large, flat sheet carries a uniformly distributed electric current with current per unit width ),. This current creates Problems nd tic nt ic e, n, f T- 1. a magnetic field on both sides of the sheet, parallel to the sheet and perpendicular to the current, with magnitude B = Mo J. If the...
Please answer all Part 1. Single Selection (3 Marks for each question. Total 30 Marks) 1. An electron is moving perpendicular to a 1.0T magnetic field. The electron has a velocity of 1 x 10 m/s. What is the magnitude of the force acting on the electron? (A) 1.6 x 10-13 N (B) 1.6 x 10-12 N (C) 1.6x10-אי (D) 1.6x10, N 2. The Points A through E on the Figurel represent various distances from the center of the current-carrying...