Question

4.4 More slits (Modified) (5 pts) Light from a distant, monochromatic source hits an opaque barrier with narrow, parallel slits. Two slits are displaced by distances ±p/2 from the centerline of the setup. Assume slit spacing p = 0:3 mm, distance d = 9 m to the screen, and visible light with ? = 600 nm. a) Get a computer to make a graph of light intensity versus screen position x for the two-slit problem. b) Now consider a new situation: The same light, in the same overall geometry, hits an opaque barrier with three narrow, parallel slits. One slit is at the centerline of the setup; the others are distances ±p from the centerline. Find a formula for the resulting illumination pattern on a distant projection screen, get a computer to graph intensity versus x, and describe in words what it would look like. [Hint: If you wish to drop a term involving $p^2$, justify doing so.] c) Consider a third situation: The same light hits an opaque barrier with four narrow, equally- spaced, parallel slits, displaced by distances ±p/2 and ±3p/2 from the centerline. Make a third graph. If you see a trend emerging, describe it. Note that for one slit: $\psi = const \times e^{i(2\pi x^2)/(2\lambda R)}$ $R = \sqrt{d^2 + x^2}$

          4.4 More slits (Modified)
(5 pts)
Light from a distant, monochromatic source hits an opaque barrier with narrow, parallel slits. Two slits
are displaced by distances ±p/2 from the centerline of the setup. Assume slit spacing p = 0:3 mm,
distance d = 9 m to the screen, and visible light with ? = 600 nm.
a) Get a computer to make a graph of light intensity versus screen position x for the two-slit
problem.
b) Now consider a new situation: The same light, in the same overall geometry, hits an opaque
barrier with three narrow, parallel slits. One slit is at the centerline of the setup; the others
are distances ±p from the centerline. Find a formula for the resulting illumination pattern on
a distant projection screen, get a computer to graph intensity versus x, and describe in words
what it would look like. [Hint: If you wish to drop a term involving $p^2$, justify doing so.]
c) Consider a third situation: The same light hits an opaque barrier with four narrow, equally-
spaced, parallel slits, displaced by distances ±p/2 and ±3p/2 from the centerline. Make a third
graph. If you see a trend emerging, describe it.
Note that for one slit:
$\psi = const \times e^{i(2\pi x^2)/(2\lambda R)}$
$R = \sqrt{d^2 + x^2}$

4.4 More slits (Modified)
(5 pts)
Light from a distant, monochromatic source hits an opaque barrier with narrow, parallel slits. Two slits
are displaced by distances ±p/2 from the centerline of the setup. Assume slit spacing p = 0:3 mm,
distance d = 9 m to the screen, and visible light with ? = 600 nm.
a) Get a computer to make a graph of light intensity versus screen position x for the two-slit
problem.
b) Now consider a new situation: The same light, in the same overall geometry, hits an opaque
barrier with three narrow, parallel slits. One slit is at the centerline of the setup; the others
are distances ±p from the centerline. Find a formula for the resulting illumination pattern on
a distant projection screen, get a computer to graph intensity versus x, and describe in words
what it would look like. [Hint: If you wish to drop a term involving p^2, justify doing so.]
c) Consider a third situation: The same light hits an opaque barrier with four narrow, equally-
spaced, parallel slits, displaced by distances ±p/2 and ±3p/2 from the centerline. Make a third
graph. If you see a trend emerging, describe it.
Note that for one slit:
ψ = const × e^i(2π x^2)/(2λ R)
R = √(d^2 + x^2)

Added by William T.

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