Double-slit problem with incident and refracted angles

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SUMMARY

The discussion centers on the double-slit problem involving incident and refracted angles, specifically analyzing the path difference formula δ=dsinθ1 - dsinθ2. Participants explore the implications of the positive and negative terms in the equation, seeking to understand the physical significance of the path difference in this context. The conversation highlights the need for clarity on the small angle approximation and its application in deriving the path difference in scenarios with both incident and refracted angles.

PREREQUISITES
  • Understanding of wave optics principles
  • Familiarity with the double-slit experiment
  • Knowledge of the small angle approximation
  • Basic trigonometry related to angles and sine functions
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  • Research the derivation of path difference in wave optics
  • Study the implications of the small angle approximation in physics
  • Explore the physical interpretation of positive and negative path differences
  • Examine variations of the double-slit experiment with different configurations
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Students of physics, educators teaching wave optics, and anyone interested in the principles of interference and diffraction in light behavior.

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Homework Statement


For the given configuration, the path difference between the 2 rays is given as δ=dsinθ1 - dsinθ2

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Homework Equations


Small angle approximation?

The Attempt at a Solution


I'm used to seeing a double-slit situation where only the exit angle is specified, and thus path difference is simply δ=dsinθ. Here, though, we have an incident and refracted θ1 and θ2. Any hints at deriving the following will be appreciated:

δ=dsinθ1 - dsinθ2
 
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Here's a question for you, why do you think one term is positive while the other is negative (i.e. what does it mean physically)?
 

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