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

AI Thread Summary
To find the focal length of a convex lens that forms a sharp image, the thin lens equation is essential: 1/f = 1/p + 1/q. In this scenario, the object is 5 cm from the lens, and the total distance from the object to the screen is 20 cm, making the image distance 15 cm. By substituting these values into the equation, the focal length can be calculated. The focal length is not simply the distance from the object to the lens but requires using both object and image distances. Understanding and applying the thin lens equation is crucial for accurate calculations in optics.
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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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