A system of two lenses forms an image of an arrow at x = X3 = 61.1 cm. The first

Question

A system of two lenses forms an image of an arrow at x = X3 = 61.1 cm. The first lens is a diverging lens located at x = 0 and has a focal length of magnitude f1 = 16.1 cm. The second lens is located at x = X2 = 27.7 cm and has an unknown focal length. The tip of the object arrow is located at (x,y) = (xc, y0) = (-39.3 cm, 21.6 cm). What is x1, the x co-ordinate of image of the arrow formed by the first lens? What is y1, the y co-ordinate of the image of the tip of the arrow formed by the first lens? I 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 negative.

Explanation / Answer

for the diverging lens

1/xo + 1/x1 = 1/F1

1/39.3 + 1/x1 = -1/16.1

1) x1 = ?11.421 cm

m1 = (-x1/xo) = y1/yo)

2) y1 = -(-11.421*21.6)/39.3 = 6.277 cm

3) for 2 lens

1/(27.7+11.421) + 1/(61.1-27.7) = 1/f2

f2 = 18.017 cm

4) y3/y1 = -(61.1-27.7)/(27.7+11.421)

y3 = ?5.359 cm

5) for the 1st lens

1/xo + 1/x1 = 1/F1

1/39.3 + 1/x1 = 1/18.017

x1 = 33.269 cm

for 2 lens

-1/(33.269-27.7) + 1/x3 = -1/16.1

x3 = 8.514 cm

real and inverted

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