A beam of light converges to a point P. 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. (b) a concave lens of focal length 16 cm.

Explanation

Here the point P on the right of the lens acts as a virutal object

`(a ) f= 20 cm`
`:. , (1)/(v ) - (1) /(u ) = (1)/( f )` `rArr (1)/( v )= (1)/(20) + (1)/(12) = (3+ 5)/( 60) = (8 )/( 60)`
`rArr v= (60)/( 8 ) = 7.5 cm`
( b) f = 16 cm u =12 cm

`:. , (1)/( v ) = (1 )/( f ) + (1)/(u ) = (1) /(-16) + (1)/( 12) = (3+ 4)/( 48) = (1)/(48)`
`rArr v= 48 cm`
Hence image is at 48 cm to the right of the lens where teh beam would converge.