Converging and Diverging Lens Problem: Finding the Focal Lengths"

[supermenscher]

I am having some trouble with this one...any help would be appreciated.

A 31.8cm focal length converging lens is 21.6cm behind a diverging lens. Parallell light strikes the diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens.

I used the lens equation to find the distance of the image and got 12.86cm, then plugged that into the lens equation for a diverging lens and got -8.061 cm. However, that answer is incorrect. Any help would be appreciated.

 

[Doc Al]

There are several ways to solve this. Let's start this way: assume the focal length of the diverging lens is -x. If so, where will image from the diverging lens be formed? (Hint: where does parallel light get focused?)

Then realize that the image formed by the first lens acts as the object for the second lens.

 

[M98Ranger]

It seems like you have correctly used the lens equation to find the distance of the image formed by the converging lens. However, when using the lens equation for the diverging lens, you need to make sure to take into account the fact that the light is now diverging after passing through the converging lens. This means that the image distance will be negative, as the light is now spreading out instead of converging.

To find the focal length of the diverging lens, you can use the formula 1/f = 1/di + 1/do, where f is the focal length, di is the image distance, and do is the object distance. In this case, the object distance is the distance between the two lenses, which is 21.6cm. Since the light is now diverging, the image distance will be negative, so you can plug in your calculated value of -12.86cm for di. Solving for f, you should get a focal length of 12.86cm for the diverging lens.

Another way to think about this problem is to consider the converging lens as a virtual object for the diverging lens. This means that the light rays leaving the converging lens will appear to be coming from a point 21.6cm in front of the diverging lens. Using this as your object distance, you can again use the lens equation to find the focal length of the diverging lens and should get the same answer of 12.86cm.

I hope this helps! Just remember to pay attention to the direction of light rays after passing through each lens, and be careful with the signs in the lens equation. Good luck!