Question

2 identical thin converging lens brought in a contact so that their axes coincide are place 12.5 cm from an object what is the optical power of the system and each lens if the real image formed by the system of lens is 4 times as large as the object​

Answer 1

10D optical power of each lens 5D.

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Answer 2

It is given that v = 4u. 

Assume that combined focal length is F. So 1/F = 1/f1 + 1/f2 where f1 and f2 are the individual focal length. Since identical lens are used -- the f1 = f2 = f (say). So 1/F = 2/f ---> f = 2F.

Now from lens equation --- 1/v + 1/u = 1/F, putting v = 4u, we get F = 4u/5. Putting u = 12.5, F = 10 cm.

So combined Power is P = 100/F = 10D

Since f = 2F, so f = 2 * 10 = 20 cm. So individual lens power is = 100/20 = 5D

Ans: Optical power of the system is 10 D and power of each lens is 5 D.

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