Modified plano-convex lens doubt

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Discussion Overview

The discussion revolves around the behavior of a modified plano-convex lens with a tilted plane surface due to a manufacturing defect. Participants explore how this tilt affects the focusing of parallel light beams, particularly in relation to the focal point and the geometry of the lens.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how a tilted plane surface can still focus light at a specific point, suggesting that the tilt merely bends the ray by a small angle.
  • Another participant seeks clarification on the term -zR, questioning its meaning in the context of the lens's geometry.
  • Some participants clarify that the plane surface is indeed tilted but remains flat, not curved.
  • A suggestion is made to consider the lens as an ideal lens combined with a wedge prism to understand the focusing behavior better.
  • One participant proposes that the tilted surface changes the angle of the converging beam and speculates that -zR represents the distance from the original focal point to the new focal point.
  • Another participant introduces the small angle approximation, sin z = z, as a potential method for analysis.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the tilt on the lens's focusing ability, with no consensus reached on the exact nature of the focal point's shift or the interpretation of -zR.

Contextual Notes

The discussion includes assumptions about the behavior of light through the modified lens and the implications of the tilt, which remain unresolved. The relationship between the tilt angle and the focal point is also not fully clarified.

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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The plane surface of the lens is still flat, right? If so, what is -zR?
 
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.
 
Think about it this way- your lens is an ideal lens plus a wedge prism. does that help?
 
AdityaDev said:
No. Plane surface is tilted at an angle z.

It's tilted, but it's not curved, right?
 
Drakkith said:
It's tilted, but it's not curved, right?
Yes. Its not curved.
 
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?
 
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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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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