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 = 8.8 cm. The second lens is located at x = x2 = 68.58 cm and has a focal length of f2 = 24.3 cm. The tip of the object arrow is located at (x,y) = (xo,yo) = (-11.4 cm, 7.9 cm).

1)

What is x1, the x co-ordinate of image of the arrow formed by the first lens?cm

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2)

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

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3)

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

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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)(1/11.4)+(1/v)=1/8.8

or v=38.58 cm

so x=38.58

2)m=v/u

=38.58/11.

=1.974

so height=8.8*1.974

=26.74

so y=-26.74

3)for the second lens,

u=68.58-38.58

=30 cm

so,

(1/30)+(1/v)=(1/24.3

or v=127.89

so x=127.89+68.58

=196.47 cm

4)magnification=127.89/30

=4.26

so height=26.73*4.26

=113.95

so y=113.95 cm

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