A parallel beam of white light falls on a convex lens. Images of violet, yellow and orange light are formed on the other side of the lens at t distances 24 cm, 30 cm and 32 cm respectively. What is the dispersive power of the material of the lens ? (Round off your answer upto two decimal places)

Answer

`00.31`

Explanation

Considering yellow to be mean colour,
`omega = ( delta _(v) - delta _(o))/( delta _(y))`

From figure,
`tan delta ~~ delta ` .....(For small angle)
`therefore delta _(v) = (x)/( v _(v)) , delta _(0) = (x)/(v _(0)) , delta y = (x)/( v _(y))`
`therefore omega = ((x)/( v _(v)) - (x)/( v _(0)))/((x)/( v _(y)))= (x (v _(0) - v _(v))/( v _(o) v _(v)))/ ((x)/( v _(y))) = ( 32 - 24)/( 32 xx 24) xx 30`
`therefore omega = ((x)/(v_(v) ) - (x)/( v _(o)))/( ( x)/( v _(y))) = (x (v _(0) - v _(v))/( v _(0) v _(v)))/((x)/( vy )) = ( 32 - 24)/( 32 xx 24) xx 30`
`= (5)/(16) = 0. 31 25 ~~ 0.31`
......... (Rounding off to 2 decimal places)