A spherical surface of radius of curvature $R$, separates air from glass (refractive index $=1.5$ ).

Question

A spherical surface of radius of curvature $R$, separates air from glass (refractive index $=1.5$ ). The centre of curvature is in the glass medium. A point object ' $O$ ' is placed in air on the optic axis of the surface, so that its real image is formed at ' $I$ ' inside glass. The line $O I$ intersects the spherical surface at $P$ and $P O=P I$. The distance $P O$ equals to\

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(d) : By applying formula for refraction by spherical surfaces,\ $	herefore \frac{\mu_{2}}{v}-\frac{\mu_{1}}{u}=\frac{\mu_{2}-\mu_{1}}{R}$\ Let $P O=x=P I$\ $\Rightarrow \frac{1.5}{x}+\frac{1}{x}=\frac{1.5-1}{R}$\ $\Rightarrow \frac{2.5}{x}=\frac{0.5}{R}, x=5 R$