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A magician during a show makes a glass lens with \(n_g=1{\cdot}47\)  disappear in a trough of liquid. What is the refractive index of the liquid? Could the liquid be water?

Answer

Let \(n_g=\)  ref. index of glass, \(n_l=\)  ref. index of liquid, \(f_l=\)  focal length of liquid
\(\frac 1{f_l}=\left(n_g-1\right)\left[\left(\frac 1{R_1}\right)-\left(\frac 1{R_2}\right)\right]\)
For \(f_l={\infty}\)  (to make glass disappear), \(n_g=n_l\) ,
\(n_l=1{\cdot}47\) , thus it will behave as a plane glass.
No, the liquid can not be water because it’s ref. index is not \(1.33.\)
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