what is the answer to this question from this years aieee(may 1st) paper physics?A thin air film is formed by putting the convex surface of a plane convex lens over a plane glass plate.with monochromatic light,this film gives an interference pattern due to reflected light from the top(convex) surface and the bottom(glass) surface of the film.

statement 1-when light reflects from the air glass plate interface,the reflected wave suffers a phase change of pi.

statement 2-the centre of the interference pattern is dark.

pls explain .

To tackle the question regarding the interference pattern created by a thin air film between a convex lens and a glass plate, let's break down the statements and analyze them step by step.

Understanding the Interference Pattern

When monochromatic light strikes the thin air film, it reflects off both the top surface of the lens (the convex surface) and the bottom surface (the glass plate). This setup leads to the formation of an interference pattern due to the superposition of the two reflected waves.

Analyzing Statement 1

Statement 1 claims that when light reflects from the air-glass plate interface, the reflected wave suffers a phase change of π (or 180 degrees). This is indeed true. When light reflects off a medium with a higher refractive index (in this case, from air to glass), it undergoes a phase shift of π. Since the glass has a higher refractive index than air, the wave reflecting off the glass plate will experience this phase change.

Examining Statement 2

Statement 2 states that the center of the interference pattern is dark. To understand why this is the case, we need to consider the conditions for constructive and destructive interference. In this scenario, the light waves reflecting from the top and bottom surfaces can interfere either constructively or destructively depending on their path difference and any phase shifts they have undergone.

• The path difference between the two waves is determined by the thickness of the air film and the angle of incidence.
• For destructive interference (which results in a dark fringe), the path difference must be an odd multiple of half the wavelength of light, which can be expressed mathematically as: Path difference = (2t + λ/2), where t is the thickness of the film and λ is the wavelength of light.

At the center of the film, where the thickness is minimal (ideally zero), the path difference is effectively λ/2 due to the phase change of π from the reflection at the air-glass interface. This results in destructive interference, leading to a dark fringe at the center of the pattern.

Conclusion of Analysis

Both statements are accurate: the reflected wave from the air-glass interface does suffer a phase change of π, and the center of the interference pattern is indeed dark due to destructive interference. This phenomenon is a classic example of thin film interference, which is widely observed in various optical applications.