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  4. The power of a thin convex lens ( a ng=1.5) is +5.0 D. When it is placed in a liquid of refractive index a ne, then it behaves as a concave lens of focal length 100 cm. The refractive index of the liquid a nl will be

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Q. The power of a thin convex lens $\left({ }_{a} n_{g}=1.5\right)$ is $+5.0\, D$. When it is placed in a liquid of refractive index ${ }_{a} n_{e}$, then it behaves as a concave lens of focal length $100\,cm$. The refractive index of the liquid $_{a} n_{l}$ will be

Ray Optics and Optical Instruments

Solution:

We have, From lens maker formula, $5=(1.5-1)\left(\frac{2}{R}\right) $ .....(i)
and $-1=\left(\frac{1.5}{n}-1\right)\left(\frac{1}{R}\right)$ ......(ii)
Dividing Eq. (i) by Eq. (ii), we get
$-5=\frac{0.5 n}{1.5-n}$
Or $-7.5+5\,n=0.5\,n$
Or $-7.5=-4.5\, n$
$\therefore { }_{a} n_{e}=n=\frac{75}{45}=\frac{5}{3}$