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Q.

The refractive index of a lens material is 1.5 and focal length f .  Due to some chemical changes in the material, its refractive index has increased by 2%.  The percentage change in its focal length is

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a

+ 4.5%

b

– 4.5%

c

+ 5.67%

d

– 5.67%

answer is D.

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Detailed Solution

1f=(μ−1) 1R1-1R2 1f∝(μ−1) μ'=μ+2%μ=1.02μ=1.02×1.5=1.53 f'f=(μ−1)(μ'−1) f'f-1=(μ−1)(μ'−1)-1 f'-ff×100=(μ−1)-(μ'−1)(μ'−1)×100 =(μ−μ')(μ'−1)×100 =(1.5−1.53)(1.53−1)×100=-5.67%
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The refractive index of a lens material is 1.5 and focal length f .  Due to some chemical changes in the material, its refractive index has increased by 2%.  The percentage change in its focal length is