A thin lens with a focal length of 687 cm has a firefly sitt

A thin lens with a focal length of 6.87 cm has a firefly sitting 11.5 cm in front of it. The height of the firefly is 5.07 mm and 57.9 cm on the other side of lens A is a thin lens B that has a focal length of 27.5 cm and shares a common axis. Is the final image (of lens B) real or virtual? What is the position of the final image relative to the lens B as a positive number? How high is the image as a positive number? Is the final image upright or inverted in relation to the firefly?

Solution

Here,

focal length , f1 = 6.87 cn

object distance , do1 = 11.5 cm

height of object , ho = 5.07 mm

f2 = 27.5 cm

d = 57.9 cm

a) for the first lens

1/f1 = 1/di1 + 1/do1

1/6.87 = 1/11.5 + 1/di1

di1 = 17.1 cm

do2 = 57.9 - 17.1

do2 = 40.8 cm

for the second lens

1/f2 = 1/40.8 + 1/di2

1/27.5 = 1/40.8 + 1/di2

di2 = 84.21 cm

the image is Real

b)

position of final image relative to lens B = di2

position of final image relative to lens B =84.21 cm

c)

le the image height is hi

hi = 5.07 * (84.21/40.8) * (17.1/11.5)

hi = 15.6 mm

the height of image is 15.6 mm

d)

the image is real and it Upright