# How are thin film interference patterns observed?

I am having a hard time studying optics. My main difficulty is how images are formed.

In Pedrotti's Introduction to Optics, he shows a diagram of this experiment:

According to the diagram, all light rays here are parallel. I think I understand the interference phenomenon that is going on here, however, I don't understand how this phenomenon is observed. The diagram shows a microscope gathering all these parallel light rays. As far as I understand, these light rays emerge parallel to each other on the other side of the microscope. An eye would focus these parallel rays on a single point on its retina. Meaning that the observer sees a point of light, leaving out the possibility of observing the interference pattern.

I can imagine that if you put an opaque surface in place of the microscope, that the pattern becomes visible, but it's not mentioned anywhere how the interference patterns have been imaged using a microscope.

Update

According to Farcher's answer, to obtain the interference pattern that is later seen in the book(using the setup in the diagram) the virtual mirror must be tilted. I drew a diagram following the path of some light rays coming from a single light source S and concluded that after division the rays are intercepted on some point X. If the incident light ray points to the right of the source, X is above M', otherwise, it's bellow.

However, Farcher also noted that there are multiple light sources. So I decided to simulate the propagation of light from multiple sources using numpy's geometry module. The result was this graph

The points on the y=10 line are a sample of the set of light sources. The tilted line is the virtual mirror M'. Each light source draws a curved line, by the method illustrated in my diagram. Here, a curved line is the set of all the X's that a given light source 'generates'.

It's my understanding that these points are acting as objects, the microscope takes their rays and focuses them, forming a real image where interference occurs once more.

I still can't make the connection between all of this and the interference pattern that Farcher showed in his answer.

The diagram in the book is a schematic to show the general paths of the rays.
The next photograph in the book illustrates the sort of fringes which might be observed with such a set up with .

Such images are called wedge fringes and are formed if the virtual image of mirror $$M$$ in the diagram which is labelled $$M'$$ is not parallel to the surfaces of $$F$$ and $$S$$ in the diagram.

So a section might, with a greatly exaggerated angle of inclination, look like this.
(Note that there are many better diagrams in your textbook.)

The fringes which are observed are fringes of equal thickness between $$M'$$ and the top of $$F$$ or $$S$$.
They are equivalent to contour lines.

Incoming ray $$CA$$ is "partially" reflected of $$M'$$ at $$A$$ as ray $$DA$$.
That ray $$CA$$ also continues to hit the top of $$F/S$$ at $$B$$ where it is reflected back as ray $$BC$$.

Rays $$AD$$ and $$BC$$ are then collected by the objective lens of the microscope.
What is evident from my diagram is that those two rays, $$AD$$ and $$BC$$, are not parallel and so to produce interference those two rays must be made to overlap which is the purpose of the microscope's optical arrangement.
In principle the eye can do this overlapping but the advantage of the microscope is that it will also magnify the image of the fringes whose separation will be small.

To observe the fringes the microscope is focussed in the vicinity of $$A$$ and the microscope eyepiece forms a "final" image at infinity.
The fringes are said to be localised in the region of the wedge, ie this the region where a detecting instrument, microscope, eye etc, must be focussed to observe the fringes.
The light emerging from the eyepiece can either enter the lens of a camera where the incoming light is focussed on the photosensitive detector to produce a real image of the fringes or the light could go into the eye and a real image is formed on the retina of the eye.

If you have studied wedge fringes and Newton's rings the microscope which is used to observe the fringes is also focussed in the region of the wedge.

• This answer is very helpful. In your diagram, is it correct to think of point A as acting analogous to a source of light? In my head, despite it only 'emits' two rays, they are later focused to an image point, as if point A was an object. – PhysicsIsBeauty Aug 23 '19 at 23:11
• @PhysicsIsBeauty For clarity I have only drawn two rays. In reality there are rays everywhere as indicted by your diagram and the rays are travelling in many directions. A is in the region where the waves which form the interference pattern originate from. – Farcher Aug 23 '19 at 23:17
• That really complicates things for me. I tried to draw some diagrams, dislocated the CA ray so that it incides at a different angle(closer to M'), what I see is a new point B' on F/S, where the new ray reflects, which is not parallel to its reflection at M'.This is rather confusing, since I can't tell which rays the microscope ends up deciding to focus on a particular point and where that point should be. – PhysicsIsBeauty Aug 23 '19 at 23:52
• Does this answer, Michelson interferometer circular fringes, help? – Farcher Aug 24 '19 at 6:35
• Your diagram is a good one and those intersection "points" are the places on which the microscope is focussed. Those places are where the rays of light, having travelled different distances, overlap - interfere. However please note that a point source is not being used - the source is extended. – Farcher Aug 24 '19 at 11:25

Picture is worth a thousand words:

Btw, different colors here does NOT represent different wavelengths - just different light rays.

• How would you picture the more realistic case of a difuse light source? That is, each point at the end of LP acting as a source, from which rays are emitted in all allowed directions. – PhysicsIsBeauty Aug 31 '19 at 20:55