Referring to Figure 4. When a f2 = +30.0cm lens is placed an unknown distance d

Question

Referring to Figure 4. When a f2 = +30.0cm lens is placed an unknown distance d to the right of the f1 = +15.0cm lens, a real image is formed a distance qf = 50.0cm to the right of the f2 = +30.0cm lens. Find the distance d, magnification M, and image height h, assuming the object is still placed n distance p = 10.0cm to the left of the f1 = +15.0cm lens. Figure 4: When a f2 = +30.0cm lens is placed a distance d to the right of the first lens, a real image is formed at qf = 50.0cm to the right of the second lens.

Explanation / Answer

apply 1/f1 = 1/p +1/q

so q = f1p/(f1-p)

q = 15* 10/(15-10)

q = 5 cm

so

for second lens

p = d-5 , q = 50 cm

1/f = 1/d-5 +1 /50

1/d-5 = 1/30 -1/50

1/d-5 = 0.01333

d-5 = 75

d = 75 +5 = 80 m
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magnification M = -v/u = -50/10 = -5

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image height hf = 5 times of h0

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