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A ray of light is incident on a thin film. As shown in the figure, M and N are two reflected rays while P and Q are two transmitted rays. Rays N and Q undergo a phase change ofπ. Correct ordering of the refractive indices is?

A.n2>n3>n1
B.n3>n2>n1
C.n3>n1>n2
D.None of these, the specified changes cannot occur.

Answer
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Hint:
The laws of reflection and refraction are essential to solve this problem. The basic requirements for reflection and refraction to occur along with how it changes the phases of the wave upon interaction should be known.

Step by step solution:
Consider the incident wave to bei,causing reflection and transmission at the interfaceI. The reflected ray is M and the transmitted ray is P. This transmitted ray P causes further reflection and transmission at interface II, giving rise to the wave N which is reflected and the wave P gets transmitted out to medium n3. The ray N undergoes a reflection at the interfaceIagain before transmitting out to medium n1. The reflected ray in this case is Q, which gets transmitted from medium n2ton3.

As per the optics, transmission between any media doesn't cause any phase change. Therefore, any of the transmitted waves don’t undergo any phase change.

Reflection from a relatively denser medium against the incident rarer medium causes a phase change of π for the reflected wave. This is the only case when a phase change will be observed, else reflection from a relatively rarer medium will not show a phase change for the reflected wave.

Let’s consider the case of N having a phase change of π.

Since N is a transmitted wave at n1, it couldn’t have happened at interfaceI.It should have had occurred at interfaceII,when incident waveiis getting reflected to N. Therefore,n2<n3.

Similarly for the case of Q having a phase change of π.

Since, N is already having a phase change ofπ,due to interaction at interfaceII,the only possible reason for the reflected wave Q from interfaceIto have phase change π is if n2>n1.
Taking all this into consideration, we have,n3>n2>n1.

 Note:
The basic conditions for phase change need to be remembered. Any mistake in the condition can produce a different result.
Relatively rarer medium means that the outgoing medium is having a lower refractive index than the incident medium and vice-versa for relatively denser medium.