What is the Focal Length of a Convex Lens for Sharp Image Formation?

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SUMMARY

The focal length of a convex lens can be determined using the thin lens equation: 1/f = 1/p + 1/q. In this scenario, the object distance (p) is 5 cm, and the total distance between the object and the screen is 20 cm, which means the image distance (q) is 15 cm. Substituting these values into the equation yields a focal length (f) of 3.75 cm. This calculation confirms that the lens effectively produces a sharp image on the screen.

PREREQUISITES
  • Understanding of the thin lens equation
  • Knowledge of object and image distances in optics
  • Familiarity with convex lens properties
  • Basic algebra for solving equations
NEXT STEPS
  • Study the derivation of the thin lens equation
  • Learn about the characteristics of convex lenses
  • Explore practical applications of lens formulas in optical devices
  • Investigate the impact of lens curvature on focal length
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Students studying optics, physics educators, and anyone interested in understanding lens behavior and image formation.

wakejosh
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Homework Statement


An object and a screen are separated by 20 cm. A convex lens is placed between them, 5 cm from the object. In this position it causes a sharp image of the object to form on the screen. What is the focal length of the lens?

The Attempt at a Solution


wouldn't it just be 5 cm since it is producing a sharp image on the screen? the distance from the object to the lense?
 
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looking at this more I think i need an equation. I don't have a book so can someone show me the equation I am looking for?
 
You need the thin lens equation:

\frac{1}{f} = \frac{1}{p} + \frac{1}{q}

where f is the focal length, p is the object distance, and q is the image distance.
 

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