Two identical diverging lenses are separated by 22 cm. The focal length of each lens is -8.5 cm. An object is located 5.0 cm to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right.
Consider the first lens,
Focal length, f = - 8.5 cm
Object distance, u = 5 cm
Consider v as the image distance.
Using the formula, 1/f = 1/v + 1/u,
1/v = 1/f - 1/u
= 1/(-8.5) - 1/5
= - 0.317
v = - 1/0.317
= - 3.148 cm
The negative sign indicates that the image formed is at the left
side of the lens
Consider the second lens,
The object distance, u' = v + 22
= 3.148 + 22 = 25.148 cm
Focal length, f = - 8.5 cm
Consider the image distance as v'
Using the formula, 1/f = 1/v + 1/u,
1/v = 1/f - 1/u
= 1/ (-8.5) - 1/(25.148)
= - 0.157
v' = - 6.353 cm
The final image is 6.353 cm left of the lens on the right
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