Question:
when the object is at distance u1 & u2 the images formed by the same lens are real n virtual image of same size .find the focal length of the lens
Answer:
1/v1 + 1/u1 = 1/f1 ….(1)
When an image is virtual
1/(-v2) + 1/u2 = 1/f ….(2)
From equation (1)
V1 = u1f/ u1 – f
Or, v1/u1 = f/u1 –f = magnification (m)
From equation (2)
V2 = u2f/ f –u2
Or, v2/u2 = f/f-u2 = magnification (m1)
If m = m1
Or, f/u1 –f = f/f-u2
Or, f = u1 + u2/2 = Focal length
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