Which Rays to Consider for Image Formation via Concave and Convex Lenses?

[PrakashPrasad]

I get terribly confused to consider which rays for determining image formation via concave and convex lens? Many times examples take 3 rays into consideration - 1) A ray passing through Focus 2) A ray passing Optical Center (center of curvature) and 3)A ray parallel to principal focus. But the all examples then do not consider 3 rays every time - some times they consider only 2 rays for image formation and I get confused which and how to determine rays to consider for image formation via concave and convex lens - is there an easy way to follow it?

 

[Drakkith]

As far as I know, you really just need two rays. With basic geometric optics that doesn't take into account aberrations, all you need to do is find where two rays emerging from a single point on the object intersect in image space. I usually use a ray parallel to the optical axis and a ray passing through the focal point of the lens/mirror.

 

[Cutter Ketch]

You can use whichever rays you know how to draw, and you can use however many it takes to answer your question. Usually you can answer your question with 2.

The reason for three (I suppose 4 if you count the optic axis) is that that is usually the number of rays we know how to draw. For example consider an object outside the focal distance of a single converging lens. From a single field point in the object plane away from the optic axis we know how to draw 3 rays:

1) a ray through the near focal point will emerge parallel to the optic axis on the far side.
2) a ray through the center of the lens won't refract and continues straight.
3) a ray parallel to the optical axis will emerge on the far side of the lens converging to the far focal point.

https://upload.wikimedia.org/wikipedia/commons/7/71/Lens3.svg

So three because that's how many we can draw without having to calculate. If you can reason with fewer, feel free.

 

[PrakashPrasad]

So three because that's how many we can draw without having to calculate. If you can reason with fewer, feel free.

Thanks for the details and it helps me to clarify a lot but I have seen image formation concluded where two rays merge after converging - the third ray might not even converge at the same point : http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/image2.html#c2

Here you can see if we consider the 3rd day : "a ray through the near focal point will emerge parallel to the optic axis on the far side." will never converge where the other 2 rays did - so how do I know which 2 rays to consider first and when should the 3rd ray not be take for image formation - is there a rule for same?

 

[jtbell]

Any two of the three "principal rays" are sufficient to locate the image, provided that you draw them correctly.

It is useful to draw the third ray also, to serve as a check on the other two.

When drawn properly, your third ray does indeed "pass through" the location where the other two rays meet. You need to extend the ray backwards from the lens, along the line that it follows after passing through the lens.

Converging lens:

(The diagram above happens to have the image at the left focal point, because the object is exactly halfway between that focal point and the lens.)

Diverging lens: