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Question:

The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal length of the lens used?

b2ca

b2ac

ac

bc

Solution:

1/v - 1/u = 1/f
1/u = 1/f - 1/v
u = vf/(1-v/f)
m = v/f
m = 1 - v/f
At v = a, m1 = 1 - a/f
At v = a + b, m2 = 1 - (a+b)/f
m2 - m1 = c = [1 - (a+b)/f] - [1 - a/f]
c = b/f
f = bc