Does Light Focus When Passing Through Converging and Diverging Lenses?

[gingerelle]

Homework Statement

A converging lens has a focal length f, and a diverging
lens has a focal length –f, which has the same magnitude
as the converging lens. They are separated by a distance
D which is greater than f, as shown. Parallel light enters
from the left. Will the light be brought to a focus, and if
so where?

(basically there are two lenses. The converging lens is on the left of the diverging lens. The two are separated by some distance d. There are parallel horizontal rays traveling to the converging lens.)

Homework Equations

1/f = 1/do + 1/di ?

The Attempt at a Solution

I'm not really sure how to approach this question, but I would like to confirm some of my thoughts first (to avoid finding out I was wrong to think a certain way later). The parallel horizontal rays that hit the converging lens should go through the lens, pass through the focal point...and all be going from the focal point and out in a diverging manner.

The light that's passed through the converging lens will then pass through the diverging lens, being refracted. This will form a virtual image in between the focal point and the diverging lens.

However, the formation of this virtual image...is that considered as light being focused?

Anyway...that's basically my thinking. Is this correct or am I missing something important?

 

[Carid]

Your logic looks impeccable to me.
The converging lens brings the light to a focus;
The diverging lens doesn't.
The question looks so easy, am I missing something?

 

[thomate1]

Your understanding of converging and diverging lenses is generally correct. When parallel light enters a converging lens, it will converge at the focal point on the other side of the lens. This is considered as light being focused because the rays are brought together at a single point.

In this scenario, the parallel light will first pass through the converging lens and then through the diverging lens. The diverging lens will cause the rays to diverge again, but they will still intersect at a point in between the focal point and the lens. This point is known as the virtual image, and it is not a physical image that can be projected onto a screen. Rather, it is an image that can only be seen by looking through the lenses.

To find the exact location of the virtual image, you can use the thin lens equation: 1/f = 1/do + 1/di. In this case, the object distance (do) is infinity (since the light rays are parallel), and the focal length (f) is known. Solving for the image distance (di) will give you the location of the virtual image.

It is important to note that in this scenario, the light is not being brought to a single focus point, but rather it is being redirected by the lenses. However, the virtual image still serves a similar purpose as a physical image in terms of focusing light and creating a clear image for the viewer.