Intensity of Double Slit Pattern

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SUMMARY

The intensity of the double slit pattern is defined by the formula I = 4Icos²(φ/2), where φ represents the phase difference between the light waves from the two slits. The derivation of this formula can be approached geometrically using a phasor diagram or algebraically by considering the complex amplitudes from each slit. The resulting expression for intensity demonstrates how the interference pattern is influenced by the phase difference, leading to constructive and destructive interference in the observed pattern.

PREREQUISITES
  • Understanding of wave interference principles
  • Familiarity with phasor diagrams
  • Knowledge of complex numbers and their applications in physics
  • Basic grasp of trigonometric identities
NEXT STEPS
  • Study the derivation of the double slit interference formula in detail
  • Explore the concept of phasor diagrams in wave mechanics
  • Learn about the implications of phase differences in wave interference
  • Investigate experimental setups for observing double slit patterns
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Students of physics, educators teaching wave mechanics, and anyone interested in the principles of light interference and its mathematical foundations.

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Homework Statement


Could anyone help me to explain how the intensity of the double Slit pattern works because I'm looking at the formula and I'm really confused...

Homework Equations


I=4Icos^2(phi/2)
A=2Ecos(phi/2)

The Attempt at a Solution

 
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What specifically do you want explained? The formula is easy to derive geometrically using the phasor diagram. Or you can do it algebraically: since only the phase difference matters, let the complex amplitude from slit one be just A (a real number). Then the complex amplitude from slit two will be Ae. The sum is therefore A(1 + e) = A(1 + cosφ + isinφ), and the magnitude squared is A²(1 + cos²φ + 2cosφ + sin²φ) = A²(2 + 2cosφ) = 2A²(2cos²(φ/2)) = 4A²cos²(φ/2).
 
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