Two lenses, with f 1 = +20.0 cm and f 2 = +30.0 cm , are placed on the x axis, a

Question

Two lenses, with f1 = +20.0 cm  and f2 = +30.0 cm , are placed on the x axis, as shown in the figure.(Figure 1) An object is fixed 50.0 cm to the left of lens 1, and lens 2 is a variable distance x to the right of lens 1. a)Find the lateral location of the final image relative to lens 2 for the case x = 135 cm . b)Find the lateral magnification of the final image relative to lens 2 for the case x = 135 cm . c)Find the lateral location of the final image relative to lens 2 for the case x = 26.6 cm . d)Find the lateral magnification of the final image relative to lens 2 for the case x = 26.6 cm . e) Find the lateral location of the final image relative to lens 2 for the case x = 0. f) Find the lateral magnification of the final image relative to lens 2 for the case x = 0. g) Show that your result for part E agrees with the relation for the effective focal length of two lenses in contact, 1/feff=1/f1+1/f2.

Explanation / Answer

given

f1 = 20 cm

f2 = 30 cm

object distance for lens 1, u1 = -50 cm

distnace between lenses = x

a. x = 135 cm

final image location wrt lens 2= v2

image location wrt lens 1 = v1

object location wrt lens2 = u2

hence

1/v1 - 1/u1 = 1/f1

1/v1 = 1/20 - 1/50

v1 = 33.333

hence

u2 = -135 + 33.33 = -101.66666666 cm

hence

v2 = 42.5 cm to the right of lens 2

b. for x = 135 cm

magnification = v2/u2 * v1/u1 = 0.27904369

c. x = 26.6 cm

u2 = 33.33 - 26.6 = 6.73 cm

hence

v2 = 5.4968 cm to the right of lens 2

d. magnification = v2/u2 * v1/u2 = -0.5444

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