How does an image formed by a cylindrical lens look like?

[fisico30]

Hello forum,

I have been trying to understand how a cylindrical lens (plano cylindrical) forms images.
The images are blurred, smeared, only in one direction. I know that this type of lens focuses parallel rays to a focal line instead of to a focal point...

So the smearing occurs along the direction of the focal line, correct?
for instance, if we look at some text through this type of lens, it will look stretched...


I have heard of spherocylindrical lenses: a lens in the shape of a football has two orthogonal meridians with different nonzero powers. A regular cylindrical lens has one of the meridians with zero power...

I have seen a picture of a sphercylindrical lens having one surface spherical and the other cylindrical...how does this lens shape compare to the football shape? do the perform the same way?

Spherocylindrical lenses have two orthogonal focal lines...

thanks
fisico30

 

[eljose79]

Hello fisico30,

Thank you for your question. As a scientist working in the field of optics, I can provide some insight into how cylindrical lenses form images and the differences between cylindrical and spherocylindrical lenses.

First, let's talk about how a cylindrical lens forms images. As you mentioned, this type of lens focuses parallel rays of light to a focal line instead of a focal point. This is due to the shape of the lens, which has a curved surface in one direction and a flat surface in the other. The curved surface causes the light to be refracted or bent, while the flat surface allows the light to pass through without any change in direction. This results in an image being formed along the focal line, which can appear blurred or stretched if the lens is not properly aligned.

You are correct in saying that the smearing or stretching of images occurs along the direction of the focal line. This is because the lens has a different refractive power in the curved direction compared to the flat direction. As a result, light passing through the lens is focused differently in these two directions, causing the image to appear distorted.

Now, let's discuss the difference between cylindrical and spherocylindrical lenses. Cylindrical lenses, as mentioned before, have one meridian with zero power and one with non-zero power. This creates a focal line in one direction. Spherocylindrical lenses, on the other hand, have two meridians with non-zero powers, resulting in two focal lines that are orthogonal to each other. This means that the lens can focus light in two different directions, allowing for correction of astigmatism in vision.

In terms of shape, a spherocylindrical lens can have one surface that is spherical and the other that is cylindrical, or both surfaces can be spherical but with different curvatures. The football shape you mentioned is one example of a spherocylindrical lens, where the two meridians have different curvatures. This shape is often used in eyeglasses for correcting astigmatism.

In summary, cylindrical lenses form images along a focal line and can cause blurring or stretching in one direction. Spherocylindrical lenses have two focal lines and are used to correct astigmatism. The shape of a spherocylindrical lens can vary, but its overall function remains the same. I hope this helps to clarify any confusion you may have had. Let me know if you