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 = 6.5 cm. The second lens is located at x = x2 = 54.24 cm and has a focal length of f2 = 20 cm. The tip of the object arrow is located at (x,y) = (xo,yo) = (-8.4 cm, 6.7 cm).

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

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

1) 1/xo + 1/x1 = 1/f1

1/8.4 + 1/x1 = 1/6.5

x1 = 28.737 cm

2)

y1/yo = x1/xo

y1 = (6.7*28.737)/8.4 = 22.92 cm

this image is formed between L1 and L2

3) 1/f2 = 1/(x2-x1) + 1/x3

1/20 = (1/(54.24-28.737)) + (1/(x3-x1))

x3 =121.424 cm

4) y3 / yo = ((x3-x1)/(x2-x1))*(x1/xo)

y3 = 83.304 cm

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