Calculate the focal length of the spectacle lens

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SUMMARY

The discussion focuses on calculating the focal length of a spectacle lens required to correct hyperopia for a person with a near point of 1.10 m. The correct formula used is 1/f = 1/p + 1/q, where p is the distance of the object (0.25 m) and q is the distance of the image. The correct focal length, after considering that the image must be on the opposite side of the lens, is determined to be 0.324 m. Participants emphasize the importance of correctly identifying the sign of q in the lens formula to arrive at the accurate focal length.

PREREQUISITES
  • Understanding of the lens formula: 1/f = 1/p + 1/q
  • Knowledge of hyperopia and its implications for vision correction
  • Familiarity with the concept of object and image distances in optics
  • Basic skills in diagramming optical systems
NEXT STEPS
  • Study the principles of geometric optics, focusing on lens equations
  • Learn about different types of lenses and their applications in vision correction
  • Explore the concept of sign conventions in optics to avoid common mistakes
  • Practice drawing ray diagrams for various optical scenarios
USEFUL FOR

Students studying optics, optometry professionals, and anyone interested in understanding vision correction methods for hyperopia.

gungo
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Homework Statement


A hyperopic eye has a near point of 1.10 m. Calculate the focal length of the spectacle lens required to correct the hyperopia (assume that the near point of the normal eye is 25.0 cm.)

Homework Equations


1/f=1/p+1/q

The Attempt at a Solution


I just used .25 m as p and 1.1 m as q and inverted it to solve for f, which gave me 0.20 m, but the answer given is 0.324 m.
 
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In order for the person to be able to clearly see an object placed 25 cm away, where should the image of the object formed by the lens be located? Should the image be on the same side of the lens as the object?
 
TSny said:
In order for the person to be able to clearly see an object placed 25 cm away, where should the image of the object formed by the lens be located? Should the image be on the same side of the lens as the object?
It should be on the opposite side, so q is negative,right? That would give the right answer.
 
gungo said:
It should be on the opposite side, so q is negative,right? That would give the right answer.
q is negative when the image is on the same side as the object.

Try to draw a diagram showing the location of the person’s head, the lens, the object, and the image. You don’t have to post the diagram, but drawing it might help.
 

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