Where is the final image in a 2 lens optics problem?

[iurod]

Homework Statement

We have a convex lens with a focal length of 8cm, which is 12cm from the second converging lens that has a focal length of 4cm. An object is 12cm from the first lens. Where is the final image?

Homework Equations

1/d_o + 1/d_i = 1/f

The Attempt at a Solution

So i know I have to apply the lens equation to both lens, starting with the first lens:

1/d_i = 1/f - 1/d_o = 1/8cm + 1/12cm = 1/24cm

d_i1=+24cm

here is where I get confused. Applying the lens equation to the second lens
I did:

1/d_i2= 1/f - 1/d_o(do here equals d_i1)
1/d_i2= 1/4cm - 1/12cm = 2/12cm

d_i2= +6cm

d_i1 + d_i2 = 30cm

The answer is 27cm, I've checked my math several times and still get the incorrect answer.

any help is greatly appreciated.

Thanks

 

[ehild]

d_i1=+24cm

here is where I get confused. Applying the lens equation to the second lens
I did:

1/d_i2= 1/f - 1/d_o(do here equals d_i1)

No, do is not equal to di1. Both the object distance and the image distance are measured from the lens. Make a drawing to see how far is the first image from the second lens and at which side. If the object is behind the lens, you have to take the object distance with negative sign.
I think that 27 cm is the distance of the final image from the object.
It is not di1+di2.

ehild

 

[iurod]

The image after the first lens is 12cm to the left of the second lens. I am confused as what is in front and behind when it comes to the second lens. Do i take the left as front and right as back (like i did for the first lens), or is this reversed when talking about the second lens?

Thank you again for your help.

 

[ehild]

It makes things clear if you draw a figure. Is the first image between the lenses, or outside?

ehild

 

[iurod]

the image is outside, all the way to the right.

 

[ehild]

So the first image would be 24 cm away from the first lens. How far is it from the second one?

ehild

 

[iurod]

it is 12 cm to the right of the second lens. So here the object is -12cm to the lens, so instead of using positive 12 for the second lens equation i should have used -12.

1/di2 = 1/4cm - 1/-12 = 4/12cm = 3cm

di1+di2 = 24cm + 3cm = 27cm

?

 

[ehild]

It is all right that di1 + di2 is 27 cm, but where is the image? You should give the reference point. So it is 27 cm away from what?

ehild

 

[iurod]

I have written in my notes that it should be 27cm from the first lens.

Question, why wouldn't it be considered 27cm from the object?

Is it when us the lens equation we are always dealing with the image length relative to the lens and not the object?

Thanks for your help!

 

[ehild]

No, it is 12 +3 cm far from the first lens, but 27 cm far from the object.

The distances in the lens equation always are meant from the lens.

ehild

 

[iurod]

Now I get it, Thank you very much for all your help ehild