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

The Correct Option is D

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, \(x=48 \,cm\)