Two systems are formed from a converging lens and a diverging lens, as shown in

Question

Two systems are formed from a converging lens and a diverging lens, as shown in parts a and b of the drawing. (The point labeled "Fconverging" is the focal point of the converging lens.) An object is placed inside the focal point of lens 1 at a distance of 8.70 cm to the left of lens 1. The focal lengths of the converging and diverging lenses are 15.0 and -20.0 cm respectively. The distance between the lenses is 50.0 cm. Determine the final image distance for each system, measured with respect to lens 2.

Explanation / Answer

1/v-1/u = 1/f

for convergign lens u = -9.6 and f = 15

so 1/v = 1/15-1/9.6 or, v = -15*9.6/5.4 = 26.67 cm to the left of converging lens

for diverging lens u = 50=26.67 = 76.67 cm

1v + 1/76.67 = -1/20 or, v = -76.67*20/(76.67+20) = 15.86 cm to the left of diverging lens i.e lens 2

iamge is formed at a distance of 15.86 cm to the left of lens 2

for system 2

1/v +1/9.6 = -1/20 or, v = 20*9.6/(20+9.6) = 6.48 cm to the left of lens 1

now for convergign lens

u = -56.48 cm

1/v +1/56.48 = 1/15

or, v = 56.48*15/(56.48-15) = 20.42 cm to the right of lens 2

image is formed at a distance of 20.42 cm to the right of lens 2

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