A system of two converging lenses forms an image of an arrow as shown. The first

Question

A system of two converging lenses forms an image of an arrow as shown. The first lens is located at x = 0 and has a focal length of f1 = 7.7 cm. The second lens is located at x = x2 = 48 cm and has a focal length of f2 = 17.2 cm. The tip of the object arrow is located at (x,y) = (xo,yo) = (-11.6 cm, 8.8 cm).

1)

2)

What is y1, the y co-ordinate of the image of the tip of the arrow formed by the first lens?

3)

What is x3, the x co-ordinate of image of the arrow formed by the two lens system?

4)

What is y3, the y co-ordinate of the image of the tip of the arrow formed by the two lens system?

Explanation / Answer

for the first lens,

1)(1/11.6)+(1/v)=1/7.7

or v=22.9 cm

so x=22.9

2)m=v/u

=22.9/11.6

=1.974

so height=8.8*1.974

=17.37

so y=-17.37

3)for the second lens,

u=48-22.9

=25.1 cm

so,

(1/25.1)+(1/v)=(1/17.2

or v=54.6481

so x=54.6481+48

=102.6481 cm

4)magnification=54.6481/25.1

=2.177

so height=17.37*2.177

=37.82

so y=37.82 cm

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