In the figure below, a pinecone is at distance p 1 = 1.6 m in front of a lens of
ID: 1609872 • Letter: I
Question
In the figure below, a pinecone is at distance p1 = 1.6 m in front of a lens of focal length f = 0.58 m. A flat mirror is at distance d = 2.2 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?
(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
p1 .... d---Explanation / Answer
a)from lens formula we know,
1/f = 1/i + 1/o
i = o x f/(o - f)
i = 1.6 x 0.58/(1.6 - 0.58) = 0.91 m
distance of this image from mirror = 2.2 - 0.91 = 1.29 m
So the second image is 1.29 m behind the mirror.
so the object distance from the lens would be,
o' = 2.2 + 1.29 = 3.49 m
again using the lens eqn
i' = o' x f / (o' - f) = 3.49 x 0.58/(3.49 - 0.58) = 0.696 m
Hence, i' = 0.696 m
b)m1 = -i/o = 0.91/1.6 = -0.57
m2 = -i'/o' = -0.696/3.49 = -0.199
M = m1 x m2 = -0.57 x -0.199 = 0.113
Hence, M = 0.113
c)Real, Upright.