Question

The question has a paragraph followed by two statements, Statement 1 and Statement 2. Of given four alternatives after the statements, choose the one that best describes the statements.
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 light reflected from the top (convex) surface and the bottom (glass plate) surface of the film.
Statement 1: When the light reflects from the air-glass plate interface, the reflected wave suffers a phase change of $\pi$

Statement 2: The center of the interference pattern is dark.
A. Statement 1 is true, Statement 2 is false.
B. Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.
C. Statement 1 is true, Statement 2 is true; Statement 2 is not the correct explanation for Statement 1.
D. Statement 1 is false, Statement 2 is true.

Answer 1

First we have to see whether statement 1 true is correct or not. Then we have to observe whether statement 2 is correct or not.
At last we have to find whether statement 2 can explain statement 1 or not.

Complete step by step solution:
First let us see how a wave is affected by interference-
Wave interference is a phenomenon that happens when passing along the same channel when two waves intersect. Interference of waves may be positive or detrimental. A standing wave pattern results from the interference of two sets of circular waves with the same frequency and the same amplitude.
Given,
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 light reflected from the top (convex) surface and the bottom (glass plate) surface of the film.
Now let us see the statement 1-
When the light reflects from the air-glass plate interface, the reflected wave suffers a phase change of $\pi$. This happens due to the phase shift that takes place as a light ray passes from air to glass and returns from the surface of glass, i.e. the one with a higher refractive index.
So, statement 1 is correct
Now let us see statement 2-
The center of the interference pattern is dark. The difference in trajectory between the reflected ray and the incident ray depends on the width of the air space between the lens and the base. Due to this the incident ray and reflected ray interact destructively. Hence, the core of the interference pattern is dark.
So, statement 2 is also correct.
Now let us see whether statement 2 is an explanation of statement 1.
As the pattern of the core is dark, we know that the difference in phase is $\left( {2n + 1} \right)\pi$.
In addition, we also understand that there is no direction variation in the middle of the interference line.
So, the distinction can therefore only be explained by reflection, which is $\pi$.

Hence, statement 2 is explanation of statement 1.
Therefore, option B is correct.

Note: Here we have to pay attention to what is given in the question. The question is for a thin air film and also the lens is a convex lens that is used. If it had been for thick film of air or concave lens the statements would have not been true.