6.59-mm-high firefly sits on the axis of, and 10.5 cm in front of, the thin lens

Question

6.59-mm-high firefly sits on the axis of, and 10.5 cm in front of, the thin lens A, whose focal length is 5.61 cm. Behind lens A there is another thin lens, lens B, with focal length 22.1 cm. The two lenses share a common axis and are 55.1 cm apart. Is the image of the firefly that lens B forms real or virtual? How far from lens B is this image located (expressed as a positive number)? What is the height of this image (as a positive number)? Is this image upright or inverted with respect to the firefly?

Explanation / Answer

h = 6.59 mm
u = -10.5cm
f= 5.61 cm

lens 1

1/v - 1/u = 1/f
1/v + 1/10.5 = 1/5.61
v = 12.046 cm
m = v/u = -1.147

lens 2

-u = 55.1 - 12.046 = 43.045 cm
f = 22.1 cm
1/v - 1/u = 1/f
v = 45.41869 cm
m = v/u = -1.05514

1. Real image [ m is -ve for both cases ]
2. v = 45.41869 cm
3. h' = mm'h = 1.147*1.00514*6.59 = 7.9755 mm
4. Upright wrt firefly [mm' > 0]

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