Convex and concave lens and paraxial rays

In summary, when light passes through a convex lens, the paraxial rays will converge at the focus on the far side. For a concave lens, the paraxial rays will refract and diverge on the far side, and if traced backwards, they will converge at the focus on the incident side. These phenomena are governed by Snell's Law, which is the solution to the least-time problem. The shape and geometry of the lens also play a role in determining the behavior of the light passing through it.
  • #1
Dustinsfl
2,281
5
What effect would a convex (concave) lens have on paraxial rays?

For a convex lens, the rays would pass through and converge on the focus on the other side.

For a concave lens, the rays would reflect back to the focus on the same side.

Is this correct?
 
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  • #2
dwsmith said:
What effect would a convex (concave) lens have on paraxial rays?

For a convex lens, the rays would pass through and converge on the focus on the other side.

I would agree.

For a concave lens, the rays would reflect back to the focus on the same side.

Is this correct?

It is not, though you might have the right idea. There would not theoretically be any reflection (though practically speaking, there's usually some reflection). We're still talking about refraction with these lenses.

Here's what would happen: the parallel rays would diverge on the far side such that, if you traced the diverging rays straight backwards through the concave lens, they would converge at the focus on the incident side.
 
  • #3
Ackbach said:
I would agree.
It is not, though you might have the right idea. There would not theoretically be any reflection (though practically speaking, there's usually some reflection). We're still talking about refraction with these lenses.

Here's what would happen: the parallel rays would diverge on the far side such that, if you traced the diverging rays straight backwards through the concave lens, they would converge at the focus on the incident side.

Can you provide a sketch of what you mean then?
 
  • #4
dwsmith said:
Can you provide a sketch of what you mean then?

Sure. This is the kind of thing I had in mind. Scroll down to Figure 16, which is about half-way down the page.
 
  • #5
Ackbach said:
Sure. This is the kind of thing I had in mind. Scroll down to Figure 16, which is about half-way down the page.

So for the convex, the paraxial rays reflect through the other side inline with the focus on the back side then, correct?
 
  • #6
dwsmith said:
So for the convex, the paraxial rays reflect through the other side inline with the focus on the back side then, correct?

I would say it like this: paraxial rays refract through a convex lens and converge at the focus on the far side.
 
  • #7
Ackbach said:
I would say it like this: paraxial rays refract through a convex lens and converge at the focus on the far side.

I mean concave not convex there and those paraxial rays reflect through on the line from the focus on their incoming side not converging to the focus on the outgoing side, correct?
 
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  • #8
dwsmith said:
I mean concave not convex there and those paraxial rays reflect

In the words of Inigo Montoya, "You keep using that word. I do not think it means what you think it means."

Reflection is when real, physical light rays bounce off something. Refraction is when real, physical light rays travel through a boundary, typically a change in the index of refraction, like the incoming or outgoing side of a lens.

When you shine light on a lens, there is hardly any reflection at all - almost all the light refracts.

You need to get this straight, because the laws governing reflection $[\theta_i=\theta_o]$ and those governing refraction $[n_i \sin(\theta_i)=n_o \sin(\theta_o)]$ are exceedingly different.

through on the line from the focus on their incoming side not converging to the focus on the outgoing side, correct?

If you use the word "refract" here instead of "reflect", then I would say you're correct. You might insert a comma after the words "incoming side".
 
  • #9
Why do the rays refract in this manner for the convex and concave lens?
 
  • #10
Well, Snell's Law, which is $n_i \sin(\theta_i)=n_o \sin(\theta_o)$, is the solution to the least-time problem (Fermat's Principle). Fundamentally, that is what is going on. You can't go more fundamental than that, to my knowledge.

That is, Snell's Law governs refraction, period. Concave and convex lenses do what they do based on the geometry of their lens grind, in conjunction with Snell's Law.
 
  • #11
Found here a lot of talks around the concave and convex subject. I'be managed to do a lot of research about the meanings regarding concave lenses. The research was made using library references but also online references. You can read about my entire research about concave lenses here: Concave Lenses - optical use and definitions - ZOOM camp.
 

Related to Convex and concave lens and paraxial rays

1. What is the difference between a convex and concave lens?

A convex lens is thicker in the middle and thinner at the edges, while a concave lens is thinner in the middle and thicker at the edges. This leads to different light-bending properties for each type of lens.

2. How do convex and concave lenses affect paraxial rays?

Convex lenses cause paraxial rays to converge (come together) at a point called the focal point, while concave lenses cause paraxial rays to diverge (spread out).

3. What is the focal length of a lens?

The focal length of a lens is the distance between the lens and its focal point. It is a measure of how strongly the lens bends light.

4. Can a lens have both convex and concave surfaces?

Yes, a lens can have both convex and concave surfaces. These types of lenses are called meniscus lenses and are used to correct for spherical aberration.

5. How are convex and concave lenses used in everyday life?

Convex lenses are commonly used in eyeglasses and magnifying glasses to correct for farsightedness and to make objects appear larger. Concave lenses are used in cameras and telescopes to help magnify distant objects.

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