# Why Does Light Not Refract at a Convex Lens's Optical Center?

• rishch
In summary: If the lens is thin then the lateral shift is negligible and the image is correctly restored.In summary, a ray of light passing through the optical center of a convex lens will not get refracted at all. The reason is that the ray is not traveling along the normal, and the lateral shift is small enough that it can be ignored.
rishch
I'd like to know why a ray of light passing through the optical center of a convex lens does not get refracted at all. According to my knowledge, a ray of light will not get refracted if the angle of incidence is zero i.e. it is along the normal. With this in mind, I see how a ray traveling along the principal axis and passing through the optical center will not get refracted at all. But why should a ray that is not traveling along the principal axis not be refracted just because it passes through the optical center. I'm almost 100% sure that it doesn't travel along the normal so why doesn't it get refracted like it should?

Consider a light ray passing through a plane sheet of glass like a window pane. If the light comes in at an angle, it goes out at the same angle, but the outgoing ray is shifted sidewise with respect to the incoming ray. The thicker the glass, the larger the shift.

The same thing happens when the ray goes through the center of a lens, because the surfaces of the lens are practically parallel near the center. When we say "a ray of light passing through the optical center of a convex lens does not get refracted" we're assuming that the lens is thin enough that the sidewise shift is small enough that we can ignore it.

Introductory treatments of optics usually focus () on ideal "thin lenses" to simplify the analysis. Analyzing real "thick lenses" takes more work. You have to look for an intermediate-level optics textbook, which usually has at least a whole chapter on thick lenses.

Ahhh...I thought it would be something like that. Yeah we learned about the lateral displacement thingamajig at school. Thanks

But the approximation would only work if the angle of incidence was quite small, otherwise the point of incidence wouldn't be near enough to the center right?

rishch said:
But the approximation would only work if the angle of incidence was quite small

Or if the lens is very thin. That's why we call it the "thin lens approximation."

Now that I think about I think it would work with any incident angle. The approximation doesn't work because near the center the rays are approximately parallel, it works because if your ray passes through the optical center, the the point of incidence and the point of emergence would be parallel making the incident ray and reflected ray parallel with insignificant lateral displacement.

And by two points being parallel, I mean, if you were to take a circle and construct a diameter you'd get points, who's tangents are parallel. In spherical mirrors, although the mirror is curved, I sometimes think of the light ray as being reflected from the tangent at the point of incidence. Thinking of it that way explains why the line from the center of curvature to any point on the mirror is the normal (as the radius to a point will be perpendicular to the tangent at that point)

I think this makes more sense then the near the center parallel idea. Am I right?

When a ray goes through the optical centre the two refracting surfaces are parallel. There is, as pointed out earlier, no change of direction but there is a lateral shift of the ray. (See this link and many others which show the path of a ray through the parallel sides of a rectangular block) This introduces distortion of the image which is only significant if the lens is 'fat'.

## 1. Why does a ray of light not get refracted at the optical center of a convex lens?

The optical center of a convex lens is the point where the principal axis intersects the lens. This point is also known as the center of curvature. When a ray of light passes through the optical center, it does not get refracted because the optical center is the thickest part of the lens. The curvature of the lens at this point is uniform, and therefore, there is no change in the direction of the light ray.

## 2. How does the shape of a convex lens affect the refraction of light at its optical center?

The shape of a convex lens is what causes light to bend or refract. The curvature of the lens is designed in such a way that it converges the light rays towards the optical center. This means that the light rays will meet at the center without getting refracted because the curvature is uniform.

## 3. Can a convex lens with a different shape still have an optical center?

Yes, a convex lens with a different shape can still have an optical center. The optical center is determined by the intersection of the principal axis and the lens, not by the shape of the lens. However, the location of the optical center may vary depending on the curvature and thickness of the lens.

## 4. What happens to a ray of light that does not pass through the optical center of a convex lens?

A ray of light that does not pass through the optical center of a convex lens will get refracted. The amount and direction of refraction will depend on the location of the incident ray and the curvature of the lens at that point. This is because the curvature of the lens is not uniform outside of the optical center, causing the light to bend towards the thicker part of the lens.

## 5. Why is the optical center of a convex lens important in understanding the behavior of light?

The optical center of a convex lens is important because it is the point at which light rays do not get refracted. This point allows us to understand how the shape and curvature of a lens can affect the refraction of light. It also helps us to determine the focal point and magnification of the lens, which are crucial in various optical applications such as cameras, telescopes, and microscopes.

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