What focal-length lens would you need to place next to a converging lens of focal length 29 cm to create an effective focal length of 14 cm for the combination?
To determine the focal length of the lens that should be placed next to the converging lens to achieve a desired effective focal length, we can use the following formula:
1/f_total = 1/f1 + 1/f2
where:
- f_total is the effective focal length of the combination
- f1 is the focal length of the first lens (converging lens)
- f2 is the focal length of the second lens (that we need to find)
In this case, we have:
1/14 cm = 1/29 cm + 1/f2
To solve for f2, let's rearrange the equation:
1/f2 = 1/14 cm - 1/29 cm
1/f2 = (29 - 14) / (14 * 29) = 15 / (14 * 29)
f2 = (14 * 29) / 15 cm
Now we can calculate f2:
f2 ≈ 27.86 cm
So, to create an effective focal length of 14 cm for the combination, you would need a lens with a focal length of approximately 27.86 cm placed next to the converging lens with a focal length of 29 cm.