A system of two lenses forms an image of an arrow at x = x 3 = 55.5 cm. The firs

Question

A system of two lenses forms an image of an arrow at x = x3 = 55.5 cm. The first lens is a diverging lens located at x = 0 and has a focal length of magnitude f1 = 8.7 cm. The second lens is located at x = x2 = 24 cm and has an unknown focal length. The tip of the object arrow is located at (x,y) = (xo, yo) = (-34 cm, 20 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 f2, the focal length of the second lens. If the lens is a converging lens, f2 is positive. If the lens is a diverging lens, f2 is negative.

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

1/34 + 1/x1 = -1/8.7

x1 = ?6.927 cm

2) y1/yo = x1/xo

y1 = (20*6.927)/34 = 4.075 cm

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

1/f2 = (1/(6.927+24)) + (1/55.5)

f2 = 19.86 cm

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

y3 = 4.302 cm

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