How Does Lens Focal Length Affect Image Size?

AI Thread Summary
The discussion focuses on determining the focal length of a lens based on the image size produced. For a real image that is twice the height of the object, the magnification is -2, leading to the use of the magnification formula and the lens formula. The initial calculation for the focal length yielded an incorrect result of 5.77cm, indicating a need to apply the correct sign conventions. The second part of the problem involves a diverging lens with the same focal length, requiring the calculation of the height of the image formed by this lens with a 5.00cm high object. Accurate application of the lens formulas and understanding of magnification are crucial for solving these optics problems.
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Homework Statement



An object is located 26.0cm from a certain lens. The lens forms a real image that is twice as high as the object.

(i) What is the focal length of this lens?

(ii) Now replace the lens used in Part 1 with another lens. The new lens is a diverging lens whose focal points are at the same distance from the lens as the focal points of the first lens. If the object is 5.00cm high, what is the height of the image formed by the new lens? The object is still located 26.0cm from the lens.

Homework Equations



Since the image is real and 2X as large, the magnification m = -2. The formula
m = -i/o
1/o + 1/i = 1/f

The Attempt at a Solution



After attempting part 1 i got 5.77cm which is incorrect.
 
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You got to take care of the sign convention.
 

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