Final answer:
By applying the thin-lens formula for both concave lenses, the final image is found to be approximately 8.6 cm in front of the second lens, which means it is located between the two lenses.
Step-by-step explanation:
To find the location of the final image produced by two concave lenses, we must use the thin-lens formula: 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the distance from the object to the lens, and di is the distance from the lens to the image.
First, we find the image formed by the first lens, using the given values: f = -16 cm (negative because it's a concave lens) and do = 20 cm. Substituting these into the thin-lens formula we get:
1/-16 = 1/20 + 1/di (for lens 1)
Solving for di, we obtain di1 = -160/9 cm ≈ -17.78 cm. This negative value means the image is virtual and located on the object's side of the lens. Since lenses are 6.5 cm apart, the image formed by the first lens is 6.5 cm - 17.78 cm = -11.28 cm from the second lens, meaning it's 11.28 cm in front of the second lens on the opposite side.
This virtual image now acts as the object for the second lens. The distance from this new object to the second lens is now the object distance, do2 = 11.28 cm. Applying the thin-lens formula again:
1/-16 = 1/11.28 + 1/di2
After calculating, we find di2 ≈ -8.6 cm which means the final image is 8.6 cm from the second lens on the same side as the object, which is between the two lenses.
Therefore, the location of the final image produced by this lens combination is between the two lenses.