A 5.61-mm-high firefly sits on the axis of, and 10.1 cm in front of, the thin le

Question

A 5.61-mm-high firefly sits on the axis of, and 10.1 cm in front of, the thin lens A, whose focal length is 5.83 cm. Behind lens A there is another thin lens, lens B, with focal length 27.3 cm. The two lenses share a common axis and are 57.1 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

Lens 1

u = - 10.1 cm (lens is converging)

f = 5.83 cm

v = uf/ (u+f) = 13.79 cm

height of image = intitial height * (f/f+u) = -7.66 mm = 7.66 mm (inverted)

Lens 2

u = 13.79 - 57.1 = - 43.51 cm

f = 27.3 cm

v = uf/ (u+f) = 73.28 cm (from second lens)

So image is virtual (opposite in direction to u) and 73.28 cm from lens B

Height of image = height after lens A * (f/f+u) = -7.66 * ( 27.3/ (27.3-43.51)) =12.9 mm (erect)

Height of image is 12.9 mm upright with respect to firefly

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