help Two converging lenses (f1 = 9.20 cm and f2 = 5.80 cm) are separated by 18.0

Question

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Two converging lenses (f1 = 9.20 cm and f2 = 5.80 cm) are separated by 18.0 cm. The lens on the left has the longer focal length. An object stands 12.2 cm to the left of the left-hand lens in the combination. Locate the final image relative to the lens on the right. Obtain the overall magnification. Is the final image real or virtual? With respect to the original object, is the final image upright or inverted and is it larger or smaller? Locate the final image relative to the lens on the right. cm Obtain the overall magnification. Is the final image real or virtual? real virtual Is the final image upright or inverted? upright inverted Is it larger or smaller? larger smaller

Explanation / Answer

Part A)

For the first lens

1/f = 1/p + 1/q

1/9.2 = 1/12.2 + 1/q

q = 37.4 cm

SInce the lenses are 18 cm apart, that first image is the object of the second lens.

It is behind the second lens by a distance of 37.4 - 18 = 19.4 cm

For the second lens

1/5.8 = 1/-19.4 + 1/q

q = 4.47 cm

The final image is 4.47 cm to the right of the second lens

Part B)

Magnification of lens 1

M = -q/p

M = -37.4/12.2

M = -3.07

Magnification of lens 2

M = -4.47/-19.4

M = .230

Total M = (-3.07)(.23)

M = -.707

Part C)
Since the values of q (image distance) are positive, the image is real

Part D)

Since the magnification is negative, the image is inverted

Part E)
Since the value of the magnification is less than 1, the image is smaller.

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