Lensmaker's Formula: Solving for Image Distance i

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The discussion revolves around using the lensmaker's formula to find the image distance (i) given a focal length (f) of 20 cm and an object distance (o) of 50 cm. The equation 1/f = 1/o + 1/i is applied, leading to the calculation that i = 100/3 cm. There is confusion regarding the verification of the result, specifically questioning how to confirm that 1/20 equals 1/50 plus 1/(100/3). The final conclusion is that the calculated image distance of 100/3 cm is correct.
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Homework Statement


A lens has a focal length of f=20cm. If an object is at o=50 cm, where is the image?



Homework Equations



1/f = 1/o + 1/i

The Attempt at a Solution



1/20 = 1/50 + 1/i

5/100 = 2/100 + 1/i

3/100 = 1/i

i = 100/3

I'm not sure how the answer could be 1/20 = 1/50 + 1/(100/3)? What am I doing wrong?
 
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The answer is i=100/3 cm (i is the image distance). Why do you suspect it's wrong?
 

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