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Answer:
A) q₂ = 75.98 cm, B) q₂' = 115.38 cm, C)
Explanation:
A) This is an exercise in geometric optics, as the two lenses are separated by a greater distance than their focal lengths from each lens, they must be worked as independent lenses.
Lens 1. More to the left
let's use the constructor equation
where f is the focal length, p and q are the distance to the object and the image, respectively,
We must assume a distance to the object to perform the calculation, suppose that the object is 50 cm from lens 1 that is further to the left of the system.
1 / q₁ = 0.04756
q₁ = 21.0227 cm
this image is the object for the second lens that has f₂ = 14.8 cm
the distance must be measured from the second lens
p₂ = 39.4 -q₁
p₂ = 39.4 -21.0227
p₂ = 18.38 cm
let's use the constructor equation
1 / q₂ = 1 / f - 1 / p2
= 0.01316
q₂ = 75.98 cm
measured from the second lens
B) the position of the final image with respect to the first lens is
q₂’= q₂ + 39.4
q₂'= 75.98 +39.4
q₂' = 115.38 cm
C) the magnification of a lens is
m = - q / p
in this case the image measured from lens 2 is q2 = 75.98 cm
the distance to the object from the first lens is p1 = 50cm
m = - 75.98 / 50
m = -1.5 X
the negative sign indicates that the image is inverted