In an experiment with a convex lens, the length of an image is \( 1\,\mathrm{cm} \), and the object length is \( 5\,\mathrm{cm} \). If the object is placed at a distance of \( 40\,\mathrm{cm} \) from the lens, then the focal length of the lens is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 6.67\,\mathrm{cm} \)
The magnification gives the image distance, and the lens formula then gives the focal length. A convex lens forms a diminished image only when the image is real and inverted, so
\( \displaystyle |m| = \frac{\text{image length}}{\text{object length}} = \frac{1}{5} = 0.2 \)
\( \displaystyle m = \frac{v}{u} \;\Rightarrow\; v = 0.2 \times 40 = 8\,\mathrm{cm} \)
Taking the object distance as \( u = -40\,\mathrm{cm} \) and the real image at \( v = +8\,\mathrm{cm} \) (Cartesian sign convention):
\( \displaystyle \frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{8} + \frac{1}{40} = \frac{6}{40} \)
\( \displaystyle f = \frac{40}{6} = 6.67\,\mathrm{cm} \)