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
Answer: (C) Readings recorded by $P_3$ person are incorrect
$f = \dfrac1P = 0.2$ m $= 20$ cm, so $2f = 40$ cm. For a real image with a convex lens (magnitudes) $\dfrac1u + \dfrac1v = \dfrac1{20}$.
- If $f < u < 2f$, the image must be beyond $2f$ ($v > 40$ cm).
- If $u > 2f$, the image lies between $f$ and $2f$.
$P_1$ (25, 96): $\frac1{25}+\frac1{96}$ gives $f\approx19.8$ cm ✓
$P_2$ (30, 62): $f\approx20.2$ cm ✓
$P_3$ (35, 37): $u$ is between $f$ and $2f$, so $v$ must exceed 40 cm (exactly $v = 46.7$ cm); $f$ from these values is $18$ cm ✗
$P_4$ (45, 35) and $P_5$ (50, 32): $u > 2f$ and $v$ between $f$ and $2f$, giving $f\approx 19.7$ cm and $19.5$ cm, within experimental error ✓
Only $P_3$'s reading is incorrect.
Solution by Sreeraj P, M.Sc Physics