The distance between a luminous object and the screen is 60 cm. A convex lens placed in between produces a three times magnified image on the screen. The focal length of the convex lens is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 11.25 cm
The image is formed on a screen, so it is real and inverted, and the object and image are on opposite sides of the lens. The object distance and the image distance together make up the 60 cm, and the magnification fixes their ratio.
\( |u| + v = 60\,\mathrm{cm} \)
\( v = 3\,|u| \)
\( 4\,|u| = 60 \;\Rightarrow\; |u| = 15\,\mathrm{cm} \)
\( v = 45\,\mathrm{cm} \)
Using the lens formula with the Cartesian sign convention (\( u = -15\,\mathrm{cm} \), \( v = +45\,\mathrm{cm} \)):
\( \displaystyle \frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{45} + \frac{1}{15} = \frac{1 + 3}{45} = \frac{4}{45} \)
\( \displaystyle f = \frac{45}{4} = 11.25\,\mathrm{cm} \)