AIIMS 2004 Physics Interference MCQ Question

In the context of the Young's double slit experiment, interference patterns are formed when coherent light waves from two slits overlap. The position of the interference fringes on the screen depends on the path difference between the light coming from the two slits.

Explanation of the Correct Answer (C)

When a thin film of mica (or any other transparent medium) is introduced in the path of one of the interfering beams, it alters the optical path length of that beam. The optical path length is defined as the product of the physical path length and the refractive index of the medium through which the light travels.

The refractive index of mica is greater than that of air (approximately $n_{mica} \approx 1.58$). When light travels through the mica film, the optical path length increases.

If the thickness of the mica film is $t$, the additional optical path length introduced by the mica film is given by:

$$\Delta L = (n_{mica} - 1) t$$

This means that the light wave traveling through the mica will experience a phase shift due to the increased path length. Specifically, this phase shift $\Delta \phi$ can be expressed as:

$$\Delta \phi = \frac{2\pi}{\lambda} \Delta L = \frac{2\pi}{\lambda} (n_{mica} - 1) t$$

In a double-slit interference pattern, the position of the bright and dark fringes is determined by the condition for constructive and destructive interference. Constructive interference occurs when the path difference is an integer multiple of the wavelength $\lambda$ of the light:

$$d \sin \theta = m\lambda \quad (m = 0, \pm 1, \pm 2, \ldots)$$

When the mica film is inserted, it introduces a phase shift that effectively shifts the entire interference pattern without changing the fringe width. The fringe width $\beta$ is determined by:

$$\beta = \frac{\lambda D}{d}$$

where $D$ is the distance from the slits to the screen, and $d$ is the separation between the slits. Since the thickness of the mica film does not affect $D$ or $d$, the fringe width remains constant. However, the pattern shifts due to the phase change.

Why Other Options Are Incorrect

• Option A (the fringe width increases): This is incorrect because the fringe width is determined by the geometry of the setup (distance between slits and distance to the screen) and does not change with the introduction of the mica film, which only shifts the pattern.

• Option B (the fringe width decreases): This option is also incorrect for the same reason as option A. The introduction of the mica film does not alter the fringe width; it only causes a shift in the pattern.

• Option D (the fringe pattern disappears): This is incorrect as well. The introduction of a thin film will not cause the interference pattern to disappear; rather, it results in a shift of the existing pattern due to the additional phase introduced by the film.

Conclusion

Thus, the correct answer is C, as the introduction of the mica film results in a shift of the fringe pattern while keeping the fringe width unchanged.