What is the path difference for light waves from two coherent sources at an angl

What is the path difference for light waves from two coherent sources at an angle of 45° to the line joining them?

What is the path difference for light waves from two coherent sources at an angle of 45° to the line joining them?

Step 1: Identify the two coherent light sources and the distance 'd' between them.
Step 2: Understand that the angle θ is given as 45° to the line joining the two sources.
Step 3: Use the formula for path difference, which is path difference = d sin θ.
Step 4: Substitute θ with 45° in the formula: path difference = d sin(45°).
Step 5: Calculate sin(45°), which is √2/2.
Step 6: Substitute sin(45°) back into the formula: path difference = d(√2/2).
Step 7: If the distance 'd' is equal to the wavelength 'λ', then replace 'd' with 'λ': path difference = √2/2 * λ.
Step 8: Simplify the expression to find the final path difference: path difference = √2λ.

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