A beam of light converges at a point P. Nnw a lens is placed in the path of the convergent beam 12cm 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 ?

Explanation

`(1)/(v) - (1)/(u) = (1)/(f) " " f = 20 ` cm , u = + 12 cm( object on the right)
`(1)/(v) = (1)/(20) + (1)/((+12)) = (20 + 12)/(20 xx 12) = (32)/(240) = (2)/(15) " " therefore v = 7.5 ` cm
A real image is formed 7.5 cm away from the lens.
b. `(1)/(v) = (1)/(f) + (1)/(u) = (1)/(-16) + (1)/(12) = (-12 + 16)/(16 xx 12) = (4)/(16 xx 12) = (1)/(48) therefore v = 48` cm
A real image is formed at 48 cm away from the lens