An object is placed at a distance of 5 cm beyond focus on the principal axis of a convex lens. The image is formed at a distance of 3 f on the other side of the lens. The value of focal length (f) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10 cm
Use the lens formula with the sign convention: the object is on the left of the lens (negative distance), the real image on the right (positive). The object is 5 cm beyond the focus, so it is \( f + 5 \) from the lens.
\( u = -(f + 5)\,\mathrm{cm} \)
\( v = +3f \)
\( \displaystyle \frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{3f} + \frac{1}{f + 5} \)
\( \displaystyle \frac{1}{f + 5} = \frac{1}{f} - \frac{1}{3f} = \frac{2}{3f} \)
\( 3f = 2(f + 5) \;\Rightarrow\; f = 10\,\mathrm{cm} \)
Shortcut: Substitute the options: for \( f = 10\,\mathrm{cm} \), the object is at \( u = -15\,\mathrm{cm} \) and \( 1/v = 1/10 - 1/15 = 1/30 \), so \( v = 30\,\mathrm{cm} = 3f \), which fits.