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d=3a. The wavelength of the monochromatic light incident upon the slits is 1= 2a/3 (in air). The lower slit is covered with a transparent film of thickness a/2 and index of refraction n = 1.80 (you can take nair as 1.00). This film also reduces the amplitude of the electromagnetic wave passing through it by half. (a) What is the change in phase introduced by the film for the wave passing through it? (b) What is the expression for the phase difference between the waves frm the two slots, as a function of O? (c) Where is the central maximum of the interference pattern, i.e., what is the value of 6 where m = 0? (Hint: Use the result above.)

d=3a. The wavelength of the monochromatic light incident upon the slits is 1= 2a/3 (in air). The lower slit is covered with a transparent film of thickness a/2 and index of refraction n = 1.80 (you can take nair as 1.00). This film also reduces the amplitude of the electromagnetic wave passing through it by half. (a) What is the change in phase introduced by the film for the wave passing through it? (b) What is the expression for the phase difference between the waves frm the two slots, as a function of O? (c) Where is the central maximum of the interference pattern, i.e., what is the value of 6 where m = 0? (Hint: Use the result above.)

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Please answer A, B, C, D, and E.

 

Consider the interference pattern from a double-slit arrangement as shown.

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d= 3a. The wavelength of the monochromatic light incident upon the slits is 1=2a/3 (in air). The lower slit is covered with a transparent film of thickness a/2 and index of refraction n= 1.80 (you can take nair as 1.00). This film also reduces the amplitude of the electromagnetic wave passing through it by half. (a) What is the change in phase introduced by the film for the wave passing through it? (b) What is the expression for the phase difference between the waves frm the two slots, as a function of O? (c) Where is the central maximum of the interference pattern, i.e., what is the value of 6 where m = 0? (Hint: Use the result above.) (d) Draw a phasor diagram for the electric field phasors of slits 1, 2, and the total field. (e) Derive an expression for the intensity I as a function of 0 and other relevant parameters. Express your answer in terms of Io, the intensity at the center of the screen where 0= 0. (Note that the center of the diffraction pattern is still at 0=0.)
Transcribed Image Text:d= 3a. The wavelength of the monochromatic light incident upon the slits is 1=2a/3 (in air). The lower slit is covered with a transparent film of thickness a/2 and index of refraction n= 1.80 (you can take nair as 1.00). This film also reduces the amplitude of the electromagnetic wave passing through it by half. (a) What is the change in phase introduced by the film for the wave passing through it? (b) What is the expression for the phase difference between the waves frm the two slots, as a function of O? (c) Where is the central maximum of the interference pattern, i.e., what is the value of 6 where m = 0? (Hint: Use the result above.) (d) Draw a phasor diagram for the electric field phasors of slits 1, 2, and the total field. (e) Derive an expression for the intensity I as a function of 0 and other relevant parameters. Express your answer in terms of Io, the intensity at the center of the screen where 0= 0. (Note that the center of the diffraction pattern is still at 0=0.)
(4) d= 3a film
Transcribed Image Text:(4) d= 3a film
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