What is the focal length of the lens? given magnification and distance

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To find the focal length of a lens for a biology student examining a bug at a magnification of +5.00, the image distance is set at 25 cm. The student initially calculates the object distance using the magnification formula, resulting in an object distance of 5 cm. However, the focal length calculation appears incorrect, leading to confusion over the virtual nature of the image. Since the image is virtual, the image distance should be considered negative in the lens formula. The correct focal length is determined to be +6.25 cm.
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Homework Statement


A biology student wishes to examine a bug at a magnificaiton of +5.00 by looking through a single lens. the student wants the image of the bug to be a distance of 25cm from the lens. what is the focal length of the lens?

Answer:+6.25cm

Homework Equations


m=-d(image)/d(object)
1/f=\frac{1}{d(object)}+\frac{1}{d(image)}


The Attempt at a Solution


first i solve for distance of object, d(object), by using the first equation:
d(object) = (25x10-2)/5

then i calculated focal length by using the second equation
f = ((1/0.5) + (1/0.25))-1 = 0.041667

i don't know what I am doing wrong
 
Physics news on Phys.org
This is a simple magnifying glass using a converging lens.
The image is VIRTUAL...what does this mean about the image distance in the equation?
 
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