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A real point object is kept at a distance of $O P = u .$ The radius of curvature of spherical surface $A P B$ is $C P = R .$ The refractive indices of the media are $n_{1}$ and $n_{2}$ which are as shown in the diagram. Then (consider only paraxial rays)

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if $n_{2} = 2 n_{1},$ the image is virtual when $R > u$

if $n_{2} > n_{1},$ the image will be always real

the image is real for all values of $u, n_{1}$ and $n_{2}$

if $n_{1} > n_{2},$ the image is virtual for all values of u

answer is A, B.

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Detailed Solution

$\frac{n_{2}}{v} - \frac{n_{1}}{(- u)} = \frac{n_{2} - n_{1}}{R}$

$\frac{n_{2}}{v} = \frac{n_{2} - n_{1}}{R} - \frac{n_{1}}{u}$

a) $f n_{1} > n_{2} \Rightarrow v i s - v e; \Rightarrow (a)$

b) $\frac{2 n_{1}}{v} = \frac{n_{1}}{R} - \frac{n_{1}}{u} \frac{2}{v} = \frac{1}{R} - \frac{1}{u} i f R > u \Rightarrow v i s - v e$

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