Question

A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam $12$ cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length $20$ cm, and (b) a concave lens of focal length $16$ cm?

Answer 1

$\left(a\right)$. According to the given case, object is virtual, $u=+12cm$

The focal length of the convex lens is $f=+20cm$.

Using lens equation, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}-\frac{1}{12}=\frac{1}{20}$

$v=7.5cm$

$\left(b\right)$. Now the focal length of the concave lens, $f=-16cm$

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}-\frac{1}{12}=\frac{1}{-16}$

$v=48cm$