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Given a convex lens of refractive index \({\mu }_{2}\) in a liquid of refractive index \({\mu }_{1},{\mu }_{1} (Shift - …

Q1

Given a convex lens of refractive index \({\mu }_{2}\) in a liquid of refractive index \({\mu }_{1},{\mu }_{1}<{\mu }_{2}\) having radii of curvature \({\mathrm{R}}_{1},{\mathrm{R}}_{2}\mathrm{and}{\mathrm{R}}_{2}\) surface is silver polished. Where should an object be placed on the optical axis so that the real and inverted image is formed at the same place.

(Shift - I Memory Based)

a

\(\frac{\left({\mu }_{2}+{\mu }_{1}\right)\left|{\mathrm{R}}_{1}\right|}{\left({\mu }_{2}-{\mu }_{1}\right)}\)

b

\(\frac{{\mu }_{1}\left|{\mathrm{R}}_{1}\right|.\left|{\mathrm{R}}_{2}\right|}{{\mu }_{2}\left(\left|{\mathrm{R}}_{1}\right|+\left|{\mathrm{R}}_{2}\right|\right)-{\mu }_{1}\left|{\mathrm{R}}_{2}\right|}\)

c

\(\frac{{\mu }_{1}\left|{\mathrm{R}}_{1}\right|.\left|{\mathrm{R}}_{2}\right|}{{\mu }_{2}\left(2\left|{\mathrm{R}}_{1}\right|+\left|{\mathrm{R}}_{2}\right|\right)-{\mu }_{1}\sqrt{\left|{\mathrm{R}}_{1}\right|\left|{\mathrm{R}}_{2}\right|}}\)

d

\(\frac{{\mu }_{1}\left|{\mathrm{R}}_{1}\right|.\left|{\mathrm{R}}_{2}\right|}{{\mu }_{2}\left(\left|{\mathrm{R}}_{1}\right|+\left|{\mathrm{R}}_{2}\right|\right)-{\mu }_{1}\left|{\mathrm{R}}_{1}\right|}\)

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