Why do we draw two rays from a same point on an object during image formation?

When we draw ray diagrams for image formation of an object through refraction or reflection we generally draw two rays emerging from a common point on the given object, by our nature of thinking (or) by true phenomenon that there will be infinite rays of light which will emerge from one single point on an object ( a point on an object's surface irrespective of size).

Why must there be an intersection of light rays emerging from same point on an object to get the image of that respective point after reflection or refraction?

What is the reason for it ? Why does it have to be intersection of those respective rays we are talking about, why can't there be an image formation of a point surface of object when only a single ray from that point is considered without any intersection of two or more rays from that respective point on object?

There are two question parts that I'll try to answer separately:

• Why must there be an intersection of rays?
• Why do we draw two rays? (And not one or ten or a million?)

You are absolutely right that from each object spot infinitely many rays emerge. Part of them, but still infinitely many, pass the optics and contribute to the image that we e.g. want to capture with a digital sensor.

As computing that paths of infinitely many rays takes infinite time, we want to reduce that to a manageable task that gives us useful results. And two rays from an object spot is just the minimum that is still useful.

Intersection

For some thing to be called an "image", we want one spot of the image to represent one spot of the object, meaning that the light rays hitting that image spot come from only one spot of the object, and all the other object spots don't contribute.

The fact that multiple rays from the same object spot intersect in this image spot is not as important as the other, related fact: that rays from other object spots miss this image spot.

If we don't get a good separation, it means that on a given image spot we see a mixture of many object spots, and that's what we call a blurry image.

So, it's separation and not so much interception what we are interested in. In most optical configurations, those two aspects coincide: the plane where the rays intersect is also the plane where the ray bundles from different object spots are best separated.

Two rays

In good-quality optical systems, all the rays from a given object spot intersect at a single image spot. Of course, this is only possible up to a given degree, but most of the time we can neglect these minor deficiencies.

So, to find the intersection point of all rays, it is enough to intersect two of them. Then we can well assume that the others also hit the same spot.

If you like, you can compute the intersection of all the other rays as well, and that's what lens designers do, when optimizing the quality goal to have all rays really meet in the same spot.

Why not one ray?

If we only look at one ray, it's impossible to reason about separation. We can't answer the question where on the ray we get the best separation of object spots, where to place our image plane.

If we choose the wrong point on the ray as the "image spot", some rays from the other object spots will also hit that image spot, thus violating the goal of separation, giving a blurry image.

Only if we intersect multiple rays coming from the same object spot, then at their intersection point we know that this object spot's rays don't disturb other image spots, meaning that we have a good separation here.

• I really thank you for spending time to answer my question but what you said about intersection is not what I asked I meant Why does it have to be intersection of rays (2 or many) ? WHY INTERSECTIO? BUT NOT A SINGLE RAY ?
– user339808
Commented Jul 5, 2022 at 16:59
• I'll extend my answer (had not recognized that aspect). Commented Jul 6, 2022 at 8:21

An optical diagram, which could be to scale, can be used to show where an image of an object is formed.
To that end two of three predictable rays are used:

• a ray passing through a focal point after passing through a lens emerges parallel to the principal axis
• a ray parallel to the principle axis after passing through a lens passes through a focal point
• a ray passes through the pole of a lens will not be deviated

Two of those predictable rays, $$OXI$$ and $$OPI$$ are used in the diagram below.

The rays come from the top of the object so where they intersect after passing through the lens is the predicted position of the bottom of the inverted image.

You quite rightly point out that there are many rays emanating from the top of the object and in the diagram those which pass through the lens, within by cone $$WOZ$$, also cross at the bottom of the inverted image.

It is much more difficult to predict that path of those other rays and so they are not used when first constructing a ray diagram.

The image formation of the middle of the object is shown below.

Now what is special about all those rays which leave the same point on an object, pass through the lens and intersect at a point (and carry onward if there is no a screen in the image plane?
All those rays take exactly the same time to travel from the object to the point of intersection.
What that means in practical terms is that at the intersection the rays arrive in phase with one another and so the intensity of the light at that point is higher than other points.

If you have only one ray then there will be no way to predict where an image is formed and there will be no build up of intensity at one particular region.

• If you have only one ray then there will be no way to predict where an image is formed and there will be no build up of intensity at one particular region. * THANK YOU SO MUCH :)
– user339808
Commented Jul 7, 2022 at 10:00