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(D) Since the beam of light is converging at point $P$,it acts as a virtual object for the concave lens. The distance of point $P$ from the lens posit

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$48$

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(D) Since the beam of light is converging at point $P$,it acts as a virtual object for the concave lens. The distance of point $P$ from the lens position is $u = +12 \,cm$ (as it is in the direction of incident light).The focal length of the concave lens is $f = -16 \,cm$.Using the lens formula:$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$Substituting the values:$\frac{1}{v} - \frac{1}{12} = \frac{1}{-16}$$\frac{1}{v} = \frac{1}{12} - \frac{1}{16}$$\frac{1}{v} = \frac{4 - 3}{48} = \frac{1}{48}$Therefore,$v = 48 \,cm$.Since the beam converges at a distance $x$ from the lens,$x = 48 \,cm$.

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