In a two-slit interference pattern, if the angle of the first order maximum is θ, what is the path difference?

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Q: In a two-slit interference pattern, if the angle of the first order maximum is θ, what is the path difference?

Solution: The path difference for the first order maximum is given by d sin θ = λ, hence the path difference is λ sin θ.

Steps: 7

Step 1: Understand that in a two-slit interference pattern, light waves from two slits can interfere with each other.
Step 2: Know that the first order maximum occurs at a specific angle θ.
Step 3: Remember that the path difference is the difference in distance traveled by the two waves from the slits to the point of observation.
Step 4: The formula for path difference at an angle θ is given by d sin θ, where d is the distance between the two slits.
Step 5: For the first order maximum, the path difference is equal to one wavelength (λ).
Step 6: Therefore, we can set up the equation: d sin θ = λ.
Step 7: Rearranging this equation gives us the path difference as λ = d sin θ.