Optics - distance between object and image

[Smile101]

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!

 

[Redbelly98]

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

 

[Smile101]

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!

 

[Redbelly98]

4=di/do

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

di = _____ ?​

 

[Smile101]

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

 

[Redbelly98]

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.

 

[Smile101]

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

 

[rl.bhat]

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

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

Multiply d_o to both sides and solve for d_o.

 

[Redbelly98]

Multiply d_o to both sides and solve for d_o.

Yes, exactly. It's just algebra at this point.

 

[Smile101]

sorry for the late reply but, thanks a lot for your help, I really appreciated it! :)