What is the maximum magnification achievable with a simple lens?

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SUMMARY

The maximum magnification achievable with a simple lens, specifically a lens from eyeglasses, is determined using the formula Mmax = 1 + 25/q, where q is the image distance. In this case, the boy scout focused sunlight on kindling at a distance of 5.2 cm, leading to a calculated focal length of 10.83 cm. The maximum magnification achieved is 3.3, while the magnification when the eye is relaxed is calculated as Mrelaxed = 25/q, resulting in 2.4. The correct application of the lens formula is crucial for accurate results.

PREREQUISITES
  • Understanding of the lens formula: 1/v - 1/u = 1/f
  • Knowledge of magnification formulas: Mmax and Mrelaxed
  • Familiarity with the concept of image distance (q) and object distance (p)
  • Basic principles of optics and light behavior
NEXT STEPS
  • Study the lens formula in detail to avoid common mistakes in sign conventions.
  • Learn about different types of lenses and their applications in optics.
  • Explore the concept of magnification in more complex optical systems.
  • Investigate the effects of varying object distances on magnification and image quality.
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Students studying optics, physics enthusiasts, and anyone interested in understanding the principles of magnification and lens behavior.

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Homework Statement



A boy scout starts a fire by using a lens from his eyeglasses to focus sunlight on kindling 5.2 cm from the lens. The boy scout has a near point of 15.2 cm. When the lens is used as a simple magnifier, give values for the following conditions. (Hint: Assume a "normal" eye.)
(a) What is the maximum magnification that can be achieved

(b) What is the magnification when the eye is relaxed

Homework Equations


1/p+1/q=1/f

Mmax= 1+ 25/q
Mrelaxed = 25/q


The Attempt at a Solution



I have tried 1/5.2 + 1/-(15.2-5.2) = 1/f
f=10.83
then I tried 1+ 25/10.83= 3.3 and 1+15.2/10.83=2.4 and both are wrong?
Please help
 
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You're using the mirror formula. You have to use the LENS formula. 1/v-1/u=1/f. Be careful about the signs of v and u. The direction of the ray of light is +ive and opposite is -ive.
 

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