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
Distance between object and screen: $D = 60 \, \text{cm}$
Magnification: $M = 3$
Image distance: $v$, Object distance: $u$
$M = \frac{v}{u} = 3 \;\;\Rightarrow\;\; v = 3u$
Also, $u+v = 60$
$u + 3u = 60 \;\;\Rightarrow\;\; 4u = 60 \;\;\Rightarrow\;\; u = 15 \, \text{cm}, \;\; v = 45 \, \text{cm}$
Lens formula: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
$\frac{1}{f} = \frac{1}{45} + \frac{1}{15} = \frac{1+3}{45} = \frac{4}{45}$
$f = \frac{45}{4} = 11.25 \, \text{cm}$
Answer: $f = 11.25 \, \text{cm}$