In an experiment with a convex lens, the length of an image is 1 cm, and the object length is 5 cm. If the object is placed at a distance of 40 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 cm
Given:
Object length, $h_1 = 5 \text{ cm}$
Image length, $h_2 = 1 \text{ cm}$
Object distance, $u = 40 \text{ cm}$
Magnification, $m = \frac{h_2}{h_1} = \frac{1}{5}$
Also, $m = \frac{v}{u}$
$\Rightarrow \frac{v}{u} = \frac{1}{5}$
$\Rightarrow v = \frac{u}{5} = \frac{40}{5} = 8 \text{ cm}$
Using lens formula: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
$\frac{1}{f} = \frac{1}{8} + \frac{1}{40} = \frac{5 + 1}{40} = \frac{6}{40} = \frac{3}{20}$
$f = \frac{20}{3} = 6.67 \text{ cm}$
Focal length, $f = 6.67 \text{ cm}$