The radii of the curvature of the spherical surfaces which is a lens

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SUMMARY

The discussion focuses on the radii of curvature of spherical surfaces in lenses and their impact on focal length and image formation. It establishes that the curvature of the lens surfaces facing the object and image are not identical, leading to different image positions when the lens is reversed. The mathematical representation of the lens behavior is described using 2x2 matrices, where the product of the matrices representing the lens surfaces does not equal when the order is reversed, except under specific conditions where the radii of curvature are equal and of opposite signs.

PREREQUISITES
  • Understanding of lens optics and focal length
  • Basic knowledge of matrix multiplication
  • Familiarity with spherical surfaces in optics
  • Concept of composite lenses in optical devices
NEXT STEPS
  • Study the principles of lens optics and image formation
  • Learn about 2x2 matrix multiplication in optical systems
  • Explore the characteristics of bi-concave and bi-convex lenses
  • Investigate the effects of lens orientation on image position
USEFUL FOR

Optics students, optical engineers, and anyone interested in understanding lens behavior and image formation in optical systems.

komal bisht
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the radii of the curvature of the spherical surfaces which is a lens of required focal length are not same. it forms image of an object. the surfaces of the lens facing the object and the image are interhanged. will the position of the image change?
 
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Welcome to PF.

This can be thought of as a composite lens like you find in the eyepiece of a telescope or microscope. What happens when you look through a telescope the wrong way?

What level is this aimed at?
Each bit of the lens can be represented by a 2x2 matrix depending on how the particular bit changes the angle and position of the light ray crossing it. The effect of the whole lens is the matrix multiplication of the matrixes.

In this case you have three elements (a curved surface, a gap through the glass and another curved surface) so the matrix for the lense would be the product of three: ABC
Turning the lens around changes the order of the matrixes to CBA
The question amounts to asking if ABC=CBA ... and, in general, that is "no".
The special case where this is equal means a special relationship between A and C which you remember are the spherical surfaces ... iirc: the radii of curvature have to be the same and and the sign of the curvatures have to be different (the lens must be bi-concave or bi-convex).

You don't have to understand how this works, so long as you know how to multiply 2x2 matrixes you can see that ABC is not CBA
 
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