Optics - distance between object and image

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A lens with a focal length of 20 cm and a magnification of 4 requires determining the distance between the object and the image. The relevant equations include magnification (m = di/do) and the lens formula (1/di + 1/do = 1/f). The discussion emphasizes solving for one variable and substituting it into the other equation to find the unknowns. By substituting di = 4(do) into the lens equation, the problem can be simplified to find do. The conversation concludes with an acknowledgment of the algebraic approach needed to solve the problem effectively.
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hello,

Homework Statement


A lens has a focal length of 20 cm and a magnification of 4. How far apart are the object and the image?

Homework Equations


m=di(image)/do(object)
1/di + 1/do = 1/f

The Attempt at a Solution


Well, I don't really know what to do, I feel like I don't have enough information. Your help will be very appreciated!
 
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Since you have 2 equations in 2 unknowns ... solve 1 equation for 1 of the unknowns, then substitute that into the 2nd equation.
 


Redbelly98 said:
Since you have 2 equations in 2 unknowns ... solve 1 equation for 1 of the unknowns, then substitute that into the 2nd equation.

Yes, I was thinking about that but how do I do it? Seeing as if i did m=di/do 4=di/do --but it leads me to a dead end

or if i used 1/di+1/do=1/f i can only go as far as 1/di+1/do=1/20 then once again i get to a dead end!
 


Smile101 said:
4=di/do

Okay, so far so good. Now solve that equation for di:

di = _____ ?​
 


Redbelly98 said:
Okay, so far so good. Now solve that equation for di:

di = _____ ?​

umm.. di=4(do) but since we don't have do we can't solve for di
 


Smile101 said:
umm.. di=4(do) but since we don't have do we can't solve for di

You can now substitute 4do for di in the other equation ... that eliminates di, leaving do as the only unknown.
 


Redbelly98 said:
You can now substitute 4do for di in the other equation ... that eliminates di, leaving do as the only unknown.

so the equation is : 1/di +1/do =1/f

1/4do + 1/do = 1/20

Now I'm guessing we want to make do single... but i have to get rid of the 4 so since I'm dividing...

1/do^2 = 1/20 - 1/4
 


Smile101 said:
so the equation is : 1/di +1/do =1/f

1/4do + 1/do = 1/20
Multiply do to both sides and solve for do.
 


rl.bhat said:
Multiply do to both sides and solve for do.

Yes, exactly. It's just algebra at this point.
 
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sorry for the late reply but, thanks a lot for your help, I really appreciated it! :)
 
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