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

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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 constructive interference?

Solution: For constructive interference in thin films, the condition is 2nt = mλ, where m is an integer.

Steps: 5

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 for constructive interference, the waves must be in phase, meaning they reinforce each other.
Step 3: Know that the path difference between the two waves is important. The path difference is given by 2nt, where n is the refractive index and t is the thickness of the film.
Step 4: For constructive interference, this path difference must equal an integer multiple of the wavelength (λ) of the light used. This is expressed as 2nt = mλ, where m is an integer (0, 1, 2, ...).
Step 5: Conclude that the condition for constructive interference in a thin film is 2nt = mλ.