Is this an oversimplification? (treating a lens as a set of prisms)

[Dark85]

Homework Statement

Is treating a lens as a set of prisms an oversimplification?

Relevant Equations

No equations.

So in my textbook, it is stated that
"The refraction of light through a lens can be understood in a simple way by considering a lens as being made up of a set of prisms"

But wouldn't this be an oversimplification? And for the ray diagrams(given below), this seems pretty far from a lens. To approximate a lens, wouldnt a good approximation be multiple small prisms rather than just a set of 3 prisms? Or instead just use the sppherical lens and one can just construct the ray diagramd by taking the normal from the centre of curvatute of each lens and working it out?

 

[DaveC426913]

Sure.

It's a simplification. Three is less than infinity.

Is it an oversimplification? Only if it is too simple to teach the desired concept. What is the desired goal here?

 

[Dark85]

The goal is to construct the ray diagrams for 3 parallel rays passing through a convex lens and to show that they converge at the focus.

 

[DaveC426913]

The goal is to construct the ray diagrams for 3 parallel rays passing through a convex lens and to show that they converge at the focus.

Does it not do that? It seems to do that quite well.

 

[kuruman]

The diagram is misleading and works if only three rays were incident on the gadget. I think it's a bad way to present the subject.

 

[Dark85]

Does it not do that? It seems to do that quite well.

Okay it may be so, but I felt using 3 prisms to approximate a lens is not so accurate...

 

[Herman Trivilino]

To approximate a lens, wouldnt a good approximation be multiple small prisms rather than just a set of 3 prisms?

The larger the number of prisms, the better the approximation.

Or instead just use the sppherical lens and one can just construct the ray diagramd by taking the normal from the centre of curvatute of each lens and working it out?

But the surface of each prism is perpendicular to the normal at the point where each ray enters or exits. That's how the approximation works.

In your diagram three prisms work for the intended purpose because only three rays are needed for the demonstration. If more rays are needed, more prisms would have to be created.

 

[Ibix]

I think the message the book is trying to convey is that lenses work on the same principles of refraction that prisms do, and that the illustrated collection of prisms would have (very) crude focusing properties. So you can see that the focusing properties of a real lens aren't something that we pull out of nowhere, but rather they are understandable in terms of things you already know.

You are correct that the "lens" illustrated is terrible. That's why we make real lenses with smooth curved surfaces.

 

[DaveC426913]

The goal is to construct the ray diagrams for 3 parallel rays passing through a convex lens and to show that they converge at the focus.

Again, it seems to achieve its goal quite well.

I don't really understand what the objection is. Three prisms is sufficient to prove the point. Four, five or 10 prisms may be a somewhat better approximation of the real thing, but it does very little more to improve on the lesson itself.

Three rays is the simplest way to prove the principle.


This is an oversimplification:

It's too simple to prove the point. Specifically because it does not show that the rays converge at the focus. Any two non-parallel lines will cross at some point. You need a minimum of three to show they all converge on the focus.

So, two prisms is too few, and four is more than necessary.

 

[Dark85]

Again, it seems to achieve its goal quite well.

I don't really understand what the objection is. Three prisms is sufficient to prove the point. Four, five or 10 prisms may be a somewhat better approximation of the real thing, but it does very little more to improve on the lesson itself.

Three rays is the simplest way to prove the principle.

I see... well thinking about it, I guess the reason I asked that question was because I was kinda annoyed with the number of approximations made by the author in the lesson. Like not only this, he made a couple of other approximations so I just wanted to check if this especially was a legible one. Anyways, thank you all for your responses!

 

[A.T.]

The diagram is misleading and works if only three rays were incident on the gadget.

It's not misleading. It merely shows the core mechanism of a lens in the simplest way possible.

I think it's a bad way to present the subject.

I think it's the perfect way to introduce the subject. Making the lens more efficient by refining the shape is the second step.