A 5.85-mm-high firefly sits on the axis of, and 10.1 cm in front of, the thin le

Question

A 5.85-mm-high firefly sits on the axis of, and 10.1 cm in front of, the thin lens A, whose focal length is 6.49 cm. Behind lens A there is another thin lens, lens B, with focal length 27.1 cm. The two lenses share a common axis and are 63.3 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 = 6.49 cm

v = uf/ (u+f) = 18.15 cm

height of image = intitial height * (f/f+u) = -10.51 mm = 10.51 mm (inverted)

Lens 2

u = 18.15 - 63.3 = - 44.8 cm

f = 27.1 cm

v = uf/ (u+f) = 68.59 cm (from second lens)

So image is virtual (opposite in direction to u) and 68.59 cm from lens B

Height of image = height after lens A * (f/f+u) = -10.51 * ( 27.1/ (27.1-44.8)) =16.09 mm (erect)

Height of image is 16.09 mm upright with respect to firefly

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