Lens Optics: Converging Lenses Question

[twalters84]

Homework Statement

Two converging lenses, the first with focal length 40 cm and the second with focal length 33 1/3 cm, are separated by 10.0 cm. An object of height 6.0 cm is placed 20.0 cm in front of the first lens. What are the size and orientation of the final image?

A. 6.0 cm, upright
B. 6.0 cm, inverted
C. 24.0 cm, upright
D. 24.0 cm, inverted
E. 1.5 cm, inverted

Homework Equations

Lens #1:

F1 = 40 cm
Do1 = 20 cm

Lens #2

F2 = 33 1/3 cm = (100 / 3) cm

The Attempt at a Solution

First, I found the image after the first lens as follows:

1 / di1 = 1 / f1 - 1 / do1 = 1 / 40 cm - 1 / 20 cm = -1 / 40 cm

di1 = -40 cm

Negative Image Distance should imply it is a virtual image on the same side as the object.

The 2nd lens is 10 cm in front of the 1st lens, so the distance between the virtual image and the 2nd lens should be 10 cm + 40 cm = 50 cm

do2 = 50 cm

Now, I attempt to find the image after the 2nd lens as follows:

1 / di2 = 1 / f2 - 1 / do2 = 1 / (100 / 3) cm - 1 / 50 cm = 1 / 100 cm

di2 = 100 cm

Now, I attempted to find the magnification.

M1 = - di1 / do1 = - (-40) / 20 = 2
M2 = - di2 / do2 = - 100 / 50 = -2
Mn = M1 x M2 = 2 x -2 = -4

Does this mean the image should be four times as small?

The answer key states the answer is 24.0 cm. However, if it was four times as small it would be 1.5 cm.

Could somebody point me in the right direction?

Thanks in advance as it is greatly appreciated.


Travis Walters

 

[hage567]

If the image was to be 4 times smaller then M would be -0.25. The negative sign tells you about orientation. If you want to work it out mathematically, magnification is also expressed as M = h'/h, where h' is the size of the image and h is the size of the object. You have found M now, and know h because it was given in the question. This will allow you to solve for h'.

 

[twalters84]

Hey

Hey there,

The only thing that is throwing me is M = -4.

That means h' = M * h = -4 * 6.0 cm = -24 cm

Obviously, it is not going to have a negative size :)

Can somebody explain to me what I am doing wrong here. After I have this negative sign figured out, I think I will understand optics a bit better.

Thanks in advance.


Travis Walters

 

[dlgoff]

Doesn't the minus sign have to do with whether the object is inverted or not? What does you text say about this?

 

[hage567]

The negative sign tells you it is inverted, which is what I meant by "orientation" in my last post. It has nothing to do with size. Like dlgoff suggested, look it up in your textbook. All of this should be explained in it.