Lens Formula Confusion: Convex Lens, Cartesian Sign Conv.

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Discussion Overview

The discussion revolves around the application of the Cartesian sign convention for a convex lens, particularly focusing on the lens formula and the implications of object and image distances in various scenarios.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant outlines the Cartesian sign convention for a convex lens, specifying how distances are measured and their signs based on direction and position relative to the principal axis.
  • The same participant asserts that when an object is placed between 2f and f, the image is formed between the pole and f on the opposite side, using the lens equation 1/f = 1/v - 1/u.
  • This participant expresses confusion regarding the implications of the signs in the equation, noting that while v and f are positive, u is negative, leading to a contradiction in their calculations.
  • Another participant suggests drawing a ray diagram to clarify the situation, indicating that v is greater than f, which leads to a negative value for f - v, consistent with u being negative.
  • A later reply acknowledges a mistake made by the first participant, suggesting a correction in their understanding.
  • Another participant responds supportively, indicating that errors are common in such discussions.

Areas of Agreement / Disagreement

The discussion reflects a moment of confusion and correction, with some agreement on the application of the sign convention, but also highlights a lack of consensus on the initial interpretation of the lens formula.

Contextual Notes

There are unresolved aspects regarding the application of the sign convention and the implications of the lens formula, particularly in the context of object placement and image formation.

anigeo
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The cartesian sign convention for a convex lens is follows:
1. All distances on the principal axis are measured from the optical center.
2. The distances measured in the direction of incident rays are positive and all the distances measured in the direction opposite to that of the incident rays are negative.
3. All distances measured above the principal axis are positive. Thus, height of an object and that of an erect image are positive and all distances measured below the principal axis are negative.

Then for a convex lens when the object is placed between 2f and f,the image is formed between pole and f on the other side.
The lens equation is 1/f=1/v-1/u.
In this case,
v,f>0 and u<0.
then 1/u=1/v-1/f=(f-v)/(vb)>0,.....BUT HOW CAN THIS BE TRUE as u<0.
 
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draw the ray diagram and notice that v > f
therefore, f-v < 0
which comes as no surprise because u < 0

what's the problem?
 
Thanks Simon,i just made a small mistake.
 
Happen to the best of us ;)
 

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