A system of two lenses forms an image of an arrow at x = x 3 = 56 cm. The first

Question

A system of two lenses forms an image of an arrow at x = x3 = 56 cm. The first lens is a diverging lens located at x = 0 and has a focal length of magnitude f1 = 9.9 cm. The second lens is located at x = x2 = 24.5 cm and has an unknown focal length. The tip of the object arrow is located at (x,y) = (xo, yo) = (-34.7 cm, 20.2 cm).

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

2)What is y1, the y-coordinate 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-coordinate of the image of the tip of the arrow formed by the two lens system?

Explanation / Answer

1) 1/f = 1/s + 1/s'

1/-9.9 = 1/20.2 + 1/s'

= -0.15

2) k'/k = s'/s

   = (-(34.7)(-0.15))/20.2

   = 0.2591

3) 0.15 + 24.5 = 24.65 = s

1/f = 1/24.65 + 1/56

   = 0.04 + 0.018

= 0.058

f = 1/0.058 = 17.24

4) k'/k = - s'/s

= (-0.2591 * 56)/24.65

   = - 0.59

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