Five persons $P_1, P_2, P_3, P_4$ and $P_5$ recorded object distance $(u)$ and image distance (v) us

Question

Five persons $P_1, P_2, P_3, P_4$ and $P_5$ recorded object distance $(u)$ and image distance (v) using same convex lens having power +5 D as $(25,96),(30,62),(35,37),(45,35)$ and $(50,32)$ respectively. Identify correct statement

Professor PC Thomas Classes · Answer

The focal length of the convex lens is $f = \frac{100}{P} = \frac{100}{+5} = +20 	ext{ cm}$. Utilizing the thin lens formula $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ alongside the standard Cartesian sign convention (where real objects have negative $u$), the formula transforms to $v = \frac{20|u|}{|u| - 20}$ for real image formations. Checking $P_3$'s reading: if $|u| = 35 	ext{ cm}$, the theoretically expected image distance is $v = \frac{20 	imes 35}{35 - 20} = \frac{700}{15} \approx 46.7 	ext{ cm}$. The recorded value of $37 	ext{ cm}$ is significantly deviating from this ideal value, identifying it as incorrect.