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  4. 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

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Q. 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 toPhysics Question Image

KCETKCET 2020Ray Optics and Optical Instruments

Solution:

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