Problem 23.61 Two lenses, one converging with focal length20.5 cm and one diverg

Question

Problem 23.61

Two lenses, one converging with focal length20.5 cm and one diverging with focal length 11.0 cm , are placed 25.0cm apart. An object is placed 60.0cm in front of the converging lens.

Part A

Find the final image distance from second lens. Follow the sign conventions.

Express your answer to two significant figures and include the appropriate units.

Part B

Determine the magnification of the final image formed. Follow the sign conventions.

Express your answer using two significant figures.

Explanation / Answer

We know,
1/f = 1/di + do

Given,
F = 20.5 cm
Distance of object (do) = 60 cm from 1st lens

1/20.5 = 1/di + 1/60
1/di = 1/20.5 - 1/60   
di = 31.13 cm

Magnification due to converging lens m1 = -di/d0 = - 31.13/60 = -0.52

The image of the first lens is the object of the second lens.
Distance of object from diverging lens = 31.13 - 25 = 6.13 cm , As this lies behind the second lens ,
Therefore d02 = -6.13 cm
Focal length f2 = -11 cm

Substituting Values -
1/f2 = 1/di2 + 1/do2
-1/11 = 1/di2 - 1/6.13
di2 = 13.85cm

Magnification due to diverging lens m2 = -di/d0 = - (13.85/-6.13) = 2.25

Final image distance from second lens = di2 = 13.85cm

b)
Final image magnification = m1*m2
Final image magnification = - 0.52 * 2.25
Final image magnification = -1.17

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