Please show all work and all steps including ray diagrams Additional information

Question

Please show all work and all steps including ray diagrams Additional information: both lenses are convex so f1 and f2 are positive. Also use equations like: p2= d-q1 And 1/q1=1/f1 -1/p1= And m=-q/p1 4. Two thin, converging lenses are placed 60 cm apart and have the same axis. The first lens has a focal length 10 cm, and the second has a focal length of 15.0 cm. If an object 6.0 cm high is placed 20 cm in front of the first lens, what are the location and size of the final image? Is it real or virtual? aaad

Explanation / Answer

lens1

object distance = p1 = 20 cm

image distance = q1 = ?

f1 = 10 cm

1/p1 + 1/q1 = 1/f1

1/20 + 1/q1 = 1/10

q1 = 20 cm

m1 = -q1/p1 = -20/20 = -1

for lens 2

object distance p2 = d-q1 = 60-20 = 40 cm

focal length f2 = 15 cm

image distance q2 = ?

1/p2 + 1/q2 = 1/f2

1/40 + 1/q2 = 1/15

q2 = 24 cm   <<<<<<============ANSWER

m2 = -q2/p2 = -24/40 = -0.6

total magnification M = m1*m2 = -y'/y

-1*-0.6 = y'/6

image height y' = 3.6 cm <<<<<========answer

image is real <<<-----answer

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