In the figure are shown two converging lenses with x 2 = 1 m. The lens on the le
ID: 1377461 • Letter: I
Question
In the figure are shown two converging lenses with x2 = 1 m. The lens on the left (Lens 1) has a focal length of 0.25 m while the one on the right (Lens 2) has a focal length of 0.2 m. An object 2.4 cm high is located x1 = 0.424 m to the left of Lens 1.
1)
Consider the image of the object formed by Lens 1. Give its distance as measured from Lens 1 and the image height.
Distance =
m
2)
Height =
cm
3)
Now consider the image formed by Lens 1 as the object for Lens 2. Locate the image formed by Lens 2 as measured from Lens 2 and give the height of the image.
Distance =
m
4)
Height =
cm
Explanation / Answer
1)
given f1 = 0.25 m
u1 = 0.424 (object distnace for first lense)
1/u1 + 1/v1 = 1/f1
1/v1 = 1/f1 - 1/u1
1/v1 = 1/0.25 - 1/0.424
v1 = 0.609 m (image distance of first lense)
2)
magnification, m1 = -v1/u1
= -0.609/0.424
= 1.44
image height = m1*object height
= 1.44*2.4
= 3.45 cm
3)
object distnce for second lense, u2 = 1 - 0.609 = 0.391 m
given f2 = 0.2 m
1/u2 + 1/v2 = 1/f2
1/v2 = 1/f2 - 1/u2
1/v2 = 1/0.2 - 1/0.391
v1 = 0.409 m (image distance of second lense)
4)
magnification, m2 = -v2/u2
= -0.409/0.391
= 1.046
image height = m2*object height
= 1.046*3.45
= 3.6 cm