Given a thin convex lens (refractive index μ2), kept in a liquid (refractive index μ1 , μ1 < μ2) having radii of curvature |R1| and |R2|. Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place ?
1
\(\frac{\mu_{1}\left|\mathrm{R}_{1}\right| \cdot\left|\mathrm{R}_{2}\right|}{\mu_{2}\left(\left|\mathrm{R}_{1}\right|+\left|\mathrm{R}_{2}\right|\right)-\mu_{1}\left|\mathrm{R}_{1}\right|}\)
2
\(\frac{\mu_{1}\left|\mathrm{R}_{1}\right| \cdot\left|\mathrm{R}_{2}\right|}{\mu_{2}\left(\left|\mathrm{R}_{1}\right|+\left|\mathrm{R}_{2}\right|\right)-\mu_{1}\left|\mathrm{R}_{2}\right|}\)
3
\(\frac{\mu_{1}\left|\mathrm{R}_{1}\right| \cdot\left|\mathrm{R}_{2}\right|}{\mu_{2}\left(2\left|\mathrm{R}_{1}\right|+\left|\mathrm{R}_{2}\right|\right)-\mu_{1} \sqrt{\left|\mathrm{R}_{1}\right| \cdot\left|\mathrm{R}_{2}\right|}}\)
4
\(\frac{\left(\mu_{2}+\mu_{1}\right)\left|R_{1}\right|}{\left(\mu_{2}-\mu_{1}\right)}\)