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

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

Options:

Correct Answer: √2λ

Solution:

Path difference = d sin θ = d sin(45°) = d(√2/2). For d = λ, path difference = √2λ.

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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