Answer:
The object distance (u) is 28.975 cm.
Step-by-step explanation:
To find the object distance in this scenario, we can use the lens formula:
1/f = 1/v - 1/u
Where:
f = focal length of the lens
v = image distance from the lens (in this case, -20.0 cm)
u = object distance from the lens (what we're trying to find)
Given that the focal length (f) of the concave lens is -30.5 cm and the image distance (v) is -20.0 cm, we can substitute these values into the lens formula:
1/-30.5 = 1/-20 - 1/u
Simplifying the equation further:
-1/30.5 = -1/20 - 1/u
To solve for u, we can cross-multiply and rearrange the equation:
-20u = 30.5*(-20) - 30.5
-20u = -610 + 30.5
-20u = -579.5
Dividing both sides by -20:
u = -579.5 / -20
u ≈ 28.975