Why Does a Ray of Light Not Get Refracted at the Optical Center of a Convex Lens?

[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?

 

[jtbell]

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.

 

[rishch]

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

 

[rishch]

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?

 

[jtbell]

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."

 

[rishch]

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?

 

[sophiecentaur]

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'.