Question

The following figure shows a beam of light converging at point $P$. When a concave lens of focal length $16 \,cm$ is introduced in the path of the beam at a place shown by dotted line such that $OP$ becomes the axis of the lens, the beam converges at a distance $x$ from the lens. The value of $x$ will be equal to

• A. 12 cm
• B. 24 cm
• C. 36 cm
• D. 48 cm

Answer 1

Answer: (D)

48 cm

Answer 2

So, here when we put the concave lens,
let the beam will converge at a distance $x=v$
Using lens formulae, we have, $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
Where $u =12\, cm$ and $f =-16\, cm$ is given
$\therefore \frac{1}{v} = \frac{1}{f} + \frac{1}{u}$
$\left( -\frac{1}{16} \right) + \left( \frac{1}{12} \right) = \frac{1}{48} \, \text{cm}$
$\Rightarrow v =48 \,cm$
Hence, $x=48 \,cm$