Refraction By Thin Lenses

Thin lenses obey the lens equation $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ in the Cartesian convention, where a converging lens has positive focal length. Here $f=+20$ cm and the real object gives $u=-30$ cm. Substituting, $\frac{1}{v}=\frac{1}{f}+\frac{1}{u}=\frac{1}{20}+\frac{1}{-30}=\frac{3-2}{60}=\frac{1}{60}$, so $v=+60$ cm. The positive image distance confirms a real image formed 60 cm beyond the lens on the side opposite the candle, which can be caught on a screen. The value 12 cm is wrong because it would arise from adding reciprocals instead of using correct signs. The value 15 cm is wrong as it is half the object distance with no physical basis here. The value 50 cm is wrong since it incorrectly sums object distance and focal length. This is the NCERT thin-lens result for an object beyond $2f$... here between $f$ and $2f$, giving a magnified real image. A magnitude check confirms $v>u$, consistent with an enlarged real image.