In a thin film interference, if the film is of thickness t and the refractive index is n, what is the condition for the first dark fringe?

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Q: In a thin film interference, if the film is of thickness t and the refractive index is n, what is the condition for the first dark fringe?

Solution: For the first dark fringe in thin film interference, the condition is 2nt = (m + 1/2)λ, where m = 0.

Steps: 6

Step 1: Understand that thin film interference occurs when light waves reflect off the top and bottom surfaces of a thin film.
Step 2: Recognize that a dark fringe appears when the waves interfere destructively, meaning they cancel each other out.
Step 3: Know that for destructive interference, the path difference between the two waves must equal an odd multiple of half the wavelength (λ/2).
Step 4: The path difference in a thin film of thickness t and refractive index n is given by 2nt (the light travels down and back up).
Step 5: Set the condition for the first dark fringe: 2nt = (m + 1/2)λ, where m is the order of the fringe. For the first dark fringe, set m = 0.
Step 6: Substitute m = 0 into the equation: 2nt = (0 + 1/2)λ, which simplifies to 2nt = (1/2)λ.