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?
The beam converges at a point 7.5 cm from the convex lens.
The beam converges at a point 48 cm from the concave lens.
Explanation
This problem involves a virtual object concept. The convergent beam would meet at point P if no lens were present. When a lens is placed in the path, P acts as a virtual object. In the Cartesian sign convention used in NCERT, for a virtual object, the object distance (u) is taken as positive because the 'object' lies on the opposite side of the lens from where the light is coming. The lens formula 1/v - 1/u = 1/f is then applied to find the image distance (v).