Object O 1 is 15.4 cm to the left of a converging lens with a 11.4-cm focal leng

Question

Object O1 is 15.4 cm to the left of a converging lens with a 11.4-cm focal length. A second lens is positioned 10.0 cm to the right of the first lens and is observed to form a virtual image at the position of the original object O1.

(a) What is the focal length of the second lens?

_____cm

b)What is the overall magnification of this system?    

c) What is the nature (i.e., real or virtual, upright or inverted) of the final image?

              a)virtual and upright

               b)real and inverted    

              c)real and upright

              d) irtual and inverted

Explanation / Answer

Here ,

for the first lens

1/f1 = 1/di1 + 1/do1

1/11.4 = 1/15.4 + 1/di1

di1 = 43.9 cm

for the second lens

object distance ,do2 = 10 - 43.9 = -33.9 cm

image distance = - 15.4 - 10 = - 25.4 cm

Using lens formula

1/f2 = 1/di2 + 1/do2

1/f2 = -1/33.9 - 1/25.4

f2 = -14.5 cm

the focal length of the second lens is -14.5 cm

b)

overall magnification = (-43.9/(15.4)) * (-25.4/(33.9))

overall magnification = 2.14

c)

for the nautre of the image

a)virtual and upright

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