A 15-cm-local-length converging lens is 20 cm to the right of a 4.0-cm local-len

Question

A 15-cm-local-length converging lens is 20 cm to the right of a 4.0-cm local-length converging lens. A 2.2-cm-tall object is distance L to the left of the 4.0-cm-local-length lens. For What value of L is the final image of this two-lens system halfway between the two lenses? Express your answer to two significant figures and include the appropriate units. What is the height of the final image? Express your answer to two significant figures and include the appropriate units. What is the orientation of the final image? upright

Explanation / Answer

Focal length of ist lens, f1 = 4 cm

focal length of 2nd lens , f2 = 15 cm

distance between lenses, d = 20 cm

height of object, h = 2.2 cm

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image distance , v2 = - 20/2 = - 10 cm

from lens formula , 1/ f2 = 1/u2 + 1/v2

1/u2 = 1/f2 - 1/v2

1/u2 = 1/15 - ( 1/-10)

1/u2 = 1/ 15 + 1/ 10

u2 = 6 cm

image distance from the ist lens, v1 = 20- 6 = 14 cm

from 1/f1 = 1/u1 + 1/ v1

1/u1 = 1/f1 - 1/v1

1/L = 1/4 - 1/14

L = 5.6 cm

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b) magnification, m = m1*m2

m= ( -v1/u1)*(-v2/u2)

m = (-14/ 5.6) *( -(-10) / 6)

= - 4.167

height of final image ,h'= m*h

= -4.167*2.2

= - 9.1674

-ve sign shows that final image will be inverted.

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