Question

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 of$\pi .$ Correct ordering of the refractive indices is?

\[A.{{n}_{2}}>{{n}_{3}}>{{n}_{1}}\]
\[B.{{n}_{3}}>{{n}_{2}}>{{n}_{1}}\]
\[C.{{n}_{3}}>{{n}_{1}}>{{n}_{2}}\]
$D.$None of these, the specified changes cannot occur.

Answer 1

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 be$i,$causing reflection and transmission at the interface\[I.\] 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 ${{n}_{3}}.$ The ray N undergoes a reflection at the interface$I$again before transmitting out to medium ${{n}_{1}}.$ The reflected ray in this case is Q, which gets transmitted from medium ${{n}_{2}}$to${{n}_{3}}.$

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 \[\pi \] 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 $\pi .$

Since N is a transmitted wave at ${{n}_{1}},$ it couldn’t have happened at interface$I.$It should have had occurred at interface$II,$when incident wave$i$is getting reflected to N. Therefore,\[{{n}_{2}}<{{n}_{3}}.\]

Similarly for the case of Q having a phase change of $\pi .$

Since, N is already having a phase change of$\pi ,$due to interaction at interface$II,$the only possible reason for the reflected wave Q from interface$I$to have phase change $\pi $ is if ${{n}_{2}}>{{n}_{1}}.$
Taking all this into consideration, we have,${{n}_{3}}>{{n}_{2}}>{{n}_{1}}.$

 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.