Question

Two converging lenses with focal lengths of 40 cm and 20 cm are 16 cm apart. A 4.0 cm -tall object is 12 cm in front of the 40 cm -focal-length lens.

Calculate the image position.

Express your answer using two significant figures.

Calculate the image height.

Express your answer using two significant figures.

Answer 1

Using lens law for the first lens

1/f = 1/p + 1/q

1/40 = 1/12 + 1/q

q = -17.14 cm

Since the lenses are 16 cm apart, that image is 33.14 cm from the second lens, and we will use that as the object

distance for the second lens

1/20 = 1/33.14 + 1/q

q = 50.4 cm

This means the final image is 50.4 cm in back of the second lens

The distance between the object and the image is adding the distance from the object to the first lens + the lens

separation + the distance the final image is away from the second lens.

D = (12 + 16 + 50.4) = 78.4 cm

The maginifcation for the first lens is -q/p = -(-17.14)/(12) = 1.43

The maginfication for the second lens is -q/p = -50.4/33.14 = -1.52

Total magnification is (1.43)(-1.52) = -2.17

So, image height is (-2.17)(4) = -8.70 cm image is inverted..