A 6.25-mm-high firefly sits on the axis of, and 11.5 cm in front of, the thin le

Question

A 6.25-mm-high firefly sits on the axis of, and 11.5 cm in front of, the thin lens A, whose focal length is 5.49 cm. Behind lens A there is another thin lens, lens B, with focal length 24.5 cm. The two lenses share a common axis and are 62.3 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

o1 = 6.25 mm

u1 = 11.5 cm

f1 = 5.49 cm

f2 = 24.5 cm

L = 62.3 cm

By Lens equation

(1/f1) = (1/u1) + (1/v1)

Substituting values for f1 and u1 , we get v1 = 10.50 cm

magnification of lens A, m1 = v1 / u1 = 0.913

also m1 = i1 / o1 => i1 = m1o1 => i1 = 5.71 mm

u2 = L - v1 = 51.8 cm

o2 = i1 = 5.71 mm

By Lens equation

(1/f2) = (1/u2) + (1/v2)

substituting values for f2 and u2, we get v2 = 46.49 cm

magnification of lens B, m2 = v2 / u2 = 0.897

Also m2 = i2/o2 => i2 = m2o2 => i2 = 5.12 mm

(A) Real

(B) v2 = 46.49 cm

(C) i2 = 5.12 mm

(D) Upright

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