How Do Two Lenses Affect the Focus of Light from Infinity?

[SoaringQuail]

Question regarding two lenses in combination - the first is a diverging lens with f = -31.5 cm, and the second is a converging lens, 14 cm away, with f = 20.0 cm. The exact question is 'Where will an object at infinity be focused?' (coming in through the diverging lens), and I kind of understand how to do it, but I have no idea how to factor in the distance of 14 cm. Please help.

 

[hage567]

If you find where the image from the diverging lens is, you use the 14 cm to help find where the "object" distance is for the converging lens so you can then find the second image distance.

 

[m2003]

Based on the information provided, an object at infinity will be focused at a distance of 18.5 cm from the second lens. This can be determined by using the thin lens equation, 1/f = 1/di + 1/do, where f is the focal length of the lens, di is the image distance, and do is the object distance.

In this case, the first lens has a negative focal length of -31.5 cm, indicating it is a diverging lens. The second lens has a positive focal length of 20.0 cm, indicating it is a converging lens. The distance between the two lenses is 14 cm.

To find the image distance, we can first calculate the object distance using the given information. Since the object is at infinity, do is equal to infinity. Therefore, 1/do = 0. Plugging this into the thin lens equation, we get 1/f = 1/di + 0. Solving for di, we get di = f = 20.0 cm.

Now, we need to factor in the distance of 14 cm between the two lenses. This distance will act as the object distance for the second lens. Plugging this into the thin lens equation, we get 1/20.0 = 1/di + 1/14. Solving for di, we get di = 18.5 cm.

Therefore, an object at infinity will be focused at a distance of 18.5 cm from the second lens. It is important to note that this is the image distance from the second lens, and the final image distance will depend on the distance of the final image from the second lens. The exact location of the final image can be determined by using the thin lens equation again, with the value of di as 18.5 cm and the distance of the final image from the second lens as the object distance.