A system of two lenses forms an image of an arrow at x = x 3 = 45.1 cm. The firs

Question

A system of two lenses forms an image of an arrow at x = x3 = 45.1 cm. The first lens is a diverging lens located at x = 0 and has a focal length of magnitude f1 = 11.6 cm. The second lens is located at x = x2 = 20.4 cm and has an unknown focal length. The tip of the object arrow is located at (x,y) = (xo, yo) = (-28.9 cm, 22.8 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 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.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

Part 1)

For the first lanes, apply 1/f = 1/p + 1/q

1/-11.6 = 1/28.9 + 1/q

q = -8.28

So x1 = -8.28 cm

Part 2)

y1/y = -q/p

y1/22.8 = -(-8.28/28.9)

y1 = 6.53 cm

Part 3)

1/f = /p + 1/q

p = 8.28 + 20.4 = 28.68

q = 45.1 - 20.4 = 24.7

1/f = 1/28.68 + 1/24.7

f = 13.3 cm

Part 4)

y3/y1 = -q/p

y3/6.53 = -24.7/28.68

y3 = -5.62 cm

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