Two converging lenses are separated by 23.60 cm. The focal length of each lens is 12.60 cm. An object is placed 35.80 cm to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right.
Answer in cm
To determine the final image distance relative to the lens on the right, we can use the lens formula:
1/f = 1/v - 1/u
where f is the focal length of the lens, v is the image distance, and u is the object distance.
Given:
Focal length of each lens (f) = 12.60 cm
Object distance (u) = 35.80 cm
To find the image distance (v) for the lens on the left, we can use the lens formula:
1/f_left = 1/v_left - 1/u_left
Substituting the known values:
1/12.60 = 1/v_left - 1/35.80
Solving for v_left:
1/v_left = 1/12.60 + 1/35.80
1/v_left = (35.80 + 12.60)/(12.60 * 35.80)
v_left = 12.60 * 35.80 / (35.80 + 12.60)
Now, to find the image distance (v_right) for the lens on the right, we need to consider the separation between the lenses.
Lens separation (d) = 23.60 cm
The image distance for the lens on the right will be the sum of the separation (d) and the image distance (v_left) for the lens on the left:
v_right = v_left + d
Substituting the values:
v_right = v_left + 23.60 cm
So, by calculating v_right, we can determine the final image distance relative to the lens on the right.