Question

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 μ is introduced in the path of one of the
superposing beams.

Answer 1

Answer to Question # 86071, Physics / Optics

If $d$ is the distance between two slits in young slit experiment, $D$ is the distance between slits and the screen on which interference picture/pattern is obtained, theta is the angle of diffraction then the condition of maxima is

$$d \sin \theta = n \lambda$$

It is for constructive interference

The condition for minima is when the path difference is the multiple of half wavelengths and given by

$$d \sin \theta = \left(n + \frac {1}{2}\right) \lambda$$

Where $n$ takes any integers including zero

Now if a film of thickness 't' and refractive index 'm' is introduced in the path of one of the sources either $S_{1}$ or $S_{2}$, then fringe shift occurs due to change of the optical path difference

$$P = S _ {2} P - \left[ S _ {1} P + m t - t \right] = S _ {2} P - S _ {1} P - (m - 1) t = \frac {y d}{(D - \{m - 1 \})}$$

The nth fringe is shifted by

$$\Delta y = \frac {D (m - 1) t}{d} = \frac {w}{\lambda (m - 1) t}$$

Where S1 and S2 are the sources,

Film is introduced at S1

P is the point of formations

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