Geometrical OpticsHard

Question

For a given lens the magnification was found to be twice as large as when the object was0.15 m distant from it as when the distance was 0.2 m. the focal length of the lens is :-

Options

A.0.05 m
B.0.10 m
C.0.15 m
D.0.20 m

Solution

     
For the object position O1, the image is formed at I1
= - 2h
and for the object position O2, the image is formed at I2
= - h =         ....(1)
Using lens formula,
          ....(2)
Given that,
u1 = - 0.15m = - 15 cm and u2 = - 0.20 m = - 20 cm
From eq. (1)

or v2 = v1       ....(3)
From eq.. (2)

or    

or   v1 = 30 cm
Putting this value of v1 and u1 in eq. (2), we get

f = + 10 cm = 0.10 m

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