In a biprism experiment, fifth dark fringe is obtained at a point. A thin transparent film of refractive index ' ' is placed in one of the interfering paths. Now 7^ th bright fringe is obtained at the same point. If ' ' is the wavelength of light used, the thickness of film is equal to

Step-by-step solution

The path difference for the n^ th dark fringe is given by x = (2n - 1) 2 . For the 5^ th dark fringe ( n = 5 ), the initial path difference at the point is: x₁ = (2(5) - 1) 2 = 4.5 When a thin transparent film of thickness t and refractive index is introduced in one of the interfering paths, the optical path changes by ( - 1)t . The new fringe at the same point is the 7^ th bright fringe. The path difference for the n^ th bright fringe is x = n . For the 7^ th bright fringe ( n = 7 ), the new path difference is: x₂