In the figure below, a pinecone is at distance p1 = 2.1 m in front of a lens of
ID: 1497221 • Letter: I
Question
In the figure below, a pinecone is at distance p1 = 2.1 m in front of a lens of focal length f = 0.66 m. A flat mirror is at distance d = 1.6 m behind the lens. Light from the pinecone passes rightward through the lens, reflects from the mirror, passes leftward through the lens, and forms a final image of the pinecone. (a) What is the distance between the lens and the final image? . m (b) What is the overall lateral magnification of the pinecone? (c) Describe the final image. (Select all that apply.) real virtual upright inverted to the left of the lens to the right of the lens .
Explanation / Answer
Part A:
Suppose that the lens is placed to the left of the mirror. The image formed by the converging lens is formed at a distance
v = (1/f - 1/p1)-1
v = [1/0.66 - 1/2.1]-1
v = 0.9625 m to the right of the lens.
or
1.6m - 0.9625m = 0.6375 m infront of the mirror.
The image formed by the mirror for this real image then at 0.6375m to the right of the mirror, or 1.6m + 0.6375 = 2.2375m to the right of the lens.
This image then results in another image formed by the lens located at a distance,
v' = (1/f - 1/p)-1 = (1/0.66 - 1/2.2375)-1 = 0.9361m to the left of the lens.
the distance between the lens and the final image is 0.9361m to the left of the lens.
Part B:
The lateral magnification, m = [-v/p1][-v'/p] = [0.9625/2.1]*[0.9361/2.2375] = +0.192
The lateral magnification, m = +0.192
Part C:
The final image is real since v' > 0;
The image is to the LEFT of the lens.
It also has the same orientation as the object since m > 0; Therefore, the image is UPRIGHT.