Modified plano-convex lens doubt

In summary, when a parallel light beam enters the lens parallel to x-axis, it will still be able to focus it at: (R/(u-1) , -zR).
  • #1
AdityaDev
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I was thinking about the situation given my text about a plano convex lens which was produced with a manufacturing defect. It's plane surface is tilted outwards by a small angle 'z'. In the text its written that when a parallel light beam enters the lens parallel to x-axis , it will still be able to focus it at:
##(R/(u-1) , -zR)## where u is refractive index of lens and R is the radius of curvature of curved surface of lens and lens is at origin with rays along x-axis starting from negative infinity. How does this happen?

My analysis: I think the tilted surface is just for bending the ray(refraction) by a small angle 'r' and now we have Plano convex lens with parallel beam of light at an angle 'r'.
 
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  • #2
The plane surface of the lens is still flat, right? If so, what is -zR?
 
  • #3
Drakkith said:
The plane surface of the lens is still flat, right? If so, what is -zR?
No. Plane surface is tilted at an angle z.
 
  • #4
Think about it this way- your lens is an ideal lens plus a wedge prism. does that help?
 
  • #5
AdityaDev said:
No. Plane surface is tilted at an angle z.

It's tilted, but it's not curved, right?
 
  • #6
Drakkith said:
It's tilted, but it's not curved, right?
Yes. Its not curved.
 
  • #7
Andy Resnick said:
Think about it this way- your lens is an ideal lens plus a wedge prism. does that help?
Igot the x-coordinate part. But how do you get the zR?
 
  • #8
Hmmm, I think your original analysis is pretty much correct. The tilted plane surface should just change the angle of the converging beam. I'm guessing -zR is the distance the new focal point is from the original focal point, but I'm not sure.
 
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  • #9
AdityaDev said:
Igot the x-coordinate part. But how do you get the zR?

How about using the small angle approximation sin z = z?
 
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1. What is a modified plano-convex lens?

A modified plano-convex lens is a type of lens that has one flat surface (plano) and one convex surface. The convex surface is curved outwards, while the flat surface remains flat. This modification allows for the lens to have different focal lengths and can be used for correcting spherical aberrations.

2. How is a modified plano-convex lens different from a regular plano-convex lens?

A regular plano-convex lens has one flat surface and one convex surface that is in the shape of a complete sphere. In a modified plano-convex lens, the convex surface is only partially curved, resulting in a different focal length and optical properties.

3. What are the common applications of modified plano-convex lenses?

Modified plano-convex lenses are commonly used in optical instruments such as microscopes, telescopes, and cameras. They are also used in laser systems for collimating and focusing laser beams. Additionally, they can be used for correcting spherical aberrations in imaging systems.

4. How is the focal length of a modified plano-convex lens determined?

The focal length of a modified plano-convex lens is determined by the radius of curvature on the convex side of the lens. The shorter the radius, the shorter the focal length will be. Additionally, the refractive index of the material used for the lens also affects the focal length.

5. Can a modified plano-convex lens be used for correcting chromatic aberrations?

No, a modified plano-convex lens is not designed for correcting chromatic aberrations. These types of lenses have a single refractive index, which means they do not have the capability to refract different colors of light at different angles. As a result, they cannot be used for correcting chromatic aberrations, which require lenses with multiple refractive indices.

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