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 = 6.1 cm. The second lens is located at x = x2 = 53.47 cm and has a focal length of f2 = 19.8 cm. The tip of the object arrow is located at (x,y) = (xo,yo) = (-7.9 cm, 3.6 cm).

1) What is x1, the x co-ordinate of image of the arrow formed by the first lens? 26.772 cm

2) What is y1, the y co-ordinate of the image of the tip of the arrow formed by the first lens? -12.2 cm

3) What is x3, the x co-ordinate of image of the arrow formed by the two lens system? 129.5 cm

4) What is y3, the y co-ordinate of the image of the tip of the arrow formed by the two lens system? *this one is unknown*

Explanation / Answer

from the lens equation

1/f = 1/u + 1/v

1/6.1 = 1/7.9 + 1/v

v = 26.772 cm

(b)

m=v/u =26.772/7.9 =3.38

hi = ho ( -v/u) = - 3.6 (3.38) = -12.2 cm

(3)

or the second lens,

u=53.47-26.772=26.698 cm

1/26.698+1/v=1/19.8

v=76.63

x=76.63 + 53.47

=130.1 cm

(d)

hi = ho (-v/u) = -12.2 (- 76.63/26.698) =35.01 cm

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