ANSWER 3 AND 4 A system of two converging lenses forms an image of an arrow as s

Question

ANSWER 3 AND 4

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 = 7.8 cm. The second lens is located at x = x2 = 47 cm and has a focal length of f2 = 17.2 cm. The tip of the object arrow is located at (x,y) = (xo,yo) = (-11.7 cm, 5.8 cm).

1)

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

23.4 cm

2)

What is y1, the y co-ordinate of the image of the tip of the arrow formed by the first lens?

-11.6 cm

3)

What is x3, the x co-ordinate of image of the arrow formed by the two lens system?

cm

4)

What is y3, the y co-ordinate of the image of the tip of the arrow formed by the two lens system?

cm

Explanation / Answer

Number 1)

Apply 1/f = 1/p + 1/q

1/7.8 = 1/11.7 + 1/q

q = 23.4 cm

x1 = 23.4

Part 2)

h'/h = -q/p

h'/5.8 = -23.4/11.7

h' = -11.6 cm

y1 = -11.6 cm

Part 3)

The first image is the object for the second lens

The lenses are 47 cm apart so the first image is 47 - 23.4 = 23.6 cm away

1/17.2 = 1/23.6 + 1/q

q = 63.4 cm

63.4 + 47 = 110.4

x3 = 110.4 cm

Part 4)

h'/h = -q/p

h'/-11.6 = -(63.4/23.6)

h' = 31.2 cm

y3 = 31.2 cm

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