An object placed at a distance of 16 cm from a convex lens produces an image of magnification m (m 1). If the object is moved towards the lens by 8 cm then again an image of magnification m is obtained. The numerical value of the focal length of the lens is

Question

An object placed at a distance of 16 cm from a convex lens produces an image of magnification m (m > 1). If the object is moved towards the lens by 8 cm then again an image of magnification m is obtained. The numerical value of the focal length of the lens is (A) 12 cm (B) 14 cm (C) 18 cm (D) 20 cm

Tardigrade Admin · Accepted Answer

Linear magnification, m=(f/f+u) As given that magnification is same for both cases this is possible if the two different values of u are of opposite sign. i.e., (f/f-16)=(-f/f-8) ⇒ 16-f=f-8 ⇒ 2 f=24 or f=12 cm

Q. An object placed at a distance of $16 c m$ from a convex lens produces an image of magnification $m (m > 1)$ . If the object is moved towards the lens by $8 c m$ then again an image of magnification $m$ is obtained. The numerical value of the focal length of the lens is

12 cm

14 cm

18 cm

20 cm

Linear magnification, $m = \frac{f}{f + u}$
As given that magnification is same for both cases this is possible if the two different values of $u$ are of opposite sign. i.e., $\frac{f}{f - 16} = \frac{- f}{f - 8}$
$\Rightarrow 16 - f = f - 8$
$\Rightarrow 2 f = 24$
or $f = 12 c m$

Q. An object placed at a distance of 16cm from a convex lens produces an image of magnification m(m>1). If the object is moved towards the lens by 8cm then again an image of magnification m is obtained. The numerical value of the focal length of the lens is