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Question

A convex lens of focal length 40cm and refractive index 32 is placed in a medium of refractive index 53, thenIt will act as a convergent lens of focal length 100cmIt will act as a divergent lens of focal length 100 cmIt will act as a divergent lens of focal length 200 cmIt will act as a convergent lens of focal length 200cm

A
It will act as a convergent lens of focal length 200cm
B
It will act as a divergent lens of focal length 100 cm
C
It will act as a divergent lens of focal length 200 cm
D
It will act as a convergent lens of focal length 100cm
Solution
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LENS MAKERS FORMULA :When a lens is immersed in a liquid: 1f1=(μgμl−1)(1R1−1R2)Where μg = refractive index of lens f = focal length of lens in airf1 = focal length of lens in liquidThe new focal length f1 is given by:f1f=(μg−1)(μgμl−1);Given: μl=53,μg=32Substituting in the formula mentioned in the concept,f1f=32−13×32×5−1=−5f1=−5×f=−5×40=−200 cm

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