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8. [15 points] Consider 3 identical long slits parallel to each other with distance $d$ between adjacent slits. These slits are narrow enough that the effect of diffraction is negligible. A laser with wavelength $\lambda$, assumed to be a plane wave with coherent phase, is incident directly on the slits, and produces an interference pattern on a distant screen. (a) Let $\phi$ be the phase difference between waves from adjacent slits arriving at a point on the screen, which is at an angle $\theta$ from the original direction of the beam. Show that $\phi = \frac{2\pi d}{\lambda} \sin \theta$. (b) Let $E_0$ be the electric field amplitude of the wave from individual slit. Draw a phasor diagram for the total wave, and show that its electric field amplitude is given by $E_{tot} = E_0(1 + 2 \cos \phi)$. (c) Calculate and plot the intensity that is measured on the screen as a function of $\phi$. (Hint: Do not forget that intensity is proportional to square of electric field amplitude.)

          8. [15 points] Consider 3 identical long slits parallel to each other with distance $d$ between
adjacent slits. These slits are narrow enough that the effect of diffraction is negligible. A laser
with wavelength $\lambda$, assumed to be a plane wave with coherent phase, is incident directly on
the slits, and produces an interference pattern on a distant screen.
(a) Let $\phi$ be the phase difference between waves from adjacent slits arriving at a point on
the screen, which is at an angle $\theta$ from the original direction of the beam. Show that
$\phi = \frac{2\pi d}{\lambda} \sin \theta$.
(b) Let $E_0$ be the electric field amplitude of the wave from individual slit. Draw a phasor
diagram for the total wave, and show that its electric field amplitude is given by
$E_{tot} = E_0(1 + 2 \cos \phi)$.
(c) Calculate and plot the intensity that is measured on the screen as a function of $\phi$.
(Hint: Do not forget that intensity is proportional to square of electric field amplitude.)

$8. [15 points] Consider 3 identical long slits parallel to each other with distance d between adjacent slits. These slits are narrow enough that the effect of diffraction is negligible. A laser with wavelength λ, assumed to be a plane wave with coherent phase, is incident directly on the slits, and produces an interference pattern on a distant screen. (a) Let ϕ be the phase difference between waves from adjacent slits arriving at a point on the screen, which is at an angle θ from the original direction of the beam. Show that ϕ = (2π d)/(λ)sinθ. (b) Let E0 be the electric field amplitude of the wave from individual slit. Draw a phasor diagram for the total wave, and show that its electric field amplitude is given by Etot = E0(1 + 2 cosϕ). (c) Calculate and plot the intensity that is measured on the screen as a function of ϕ. (Hint: Do not forget that intensity is proportional to square of electric field amplitude.)$

Added by Frederick E.

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