Obtain the conditions for observing maxima and minima in a young two-slit interference pattern. show that these conditions change when a thin transparent sheet of thickness t and refractive index m is introduced in the path of one of the superposing beams.
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The condition for observing :
Minima — If the path difference is a multiple of half the wavelength.
Maxima — If path difference is an integral multiple of the wavelength thus waves interfere constructively.
When a film of thickness 't' and refractive index 'm' is introduced in the path of one of the sources then fringe shift occurs as the optical path difference changes.
Let the two sources be S₁ and S₂. Let the film be introduced at S₁ and P be the point of formation of the fringes, then the optical path difference at :
P = S₂P - [S₁P + mt - t] = S₂P - S₁P - (m - 1)t = y.d /{D - (m - 1)
The nth fringe is shifted by Δy = D(m - 1)t / d = w / {lambda (m - 1)t)
Minima — If the path difference is a multiple of half the wavelength.
Maxima — If path difference is an integral multiple of the wavelength thus waves interfere constructively.
When a film of thickness 't' and refractive index 'm' is introduced in the path of one of the sources then fringe shift occurs as the optical path difference changes.
Let the two sources be S₁ and S₂. Let the film be introduced at S₁ and P be the point of formation of the fringes, then the optical path difference at :
P = S₂P - [S₁P + mt - t] = S₂P - S₁P - (m - 1)t = y.d /{D - (m - 1)
The nth fringe is shifted by Δy = D(m - 1)t / d = w / {lambda (m - 1)t)
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