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 7.60 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

A)
f1 = 15 cm

u1 = 7.6 cm (object distance for first lense)

Apply,

1/u1 + 1/v1 = 1/f1

1/v1 = 1/f1 - 1/u1

1/v1 = 1/(15) - 1/7.6

v1 = -15.4 cm (image distance for first lense)

object disatnce for second lense, u2 = -(50+15.4) = -65.4 cm

f2 = -20 cm

Again Apply

1/u2 + 1/v2 = 1/f2

1/v2 = 1/f2 - 1/u2

1/v2 = 1/(-20) - 1/(-65.4)

v2 = -28.8 cm ((image distance for second lense) <<<<<<<<--------Answer

b)
f1 = -20 cm

u1 = 7.6 cm (object distance for first lense)

Apply,

1/u1 + 1/v1 = 1/f1

1/v1 = 1/f1 - 1/u1

1/v1 = 1/(-20) - 1/7.6

v1 = -5.5 cm (image distance for first lense)

object disatnce for second lense, u2 = -(50+5.5) = -55.5 cm

f2 = 15 cm

Again Apply

1/u2 + 1/v2 = 1/f2

1/v2 = 1/f2 - 1/u2

1/v2 = 1/15 - 1/(-55.5)

v2 = 11.8 cm ((image distance for second lense) <<<<---Answer

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