The focal lengths of a convex lens for red, yellow and violet rays are 100 cm, 98 cm and 96 cm respectively. Find the dispersive power of the material of the lens.

Answer

`(99)/(4900)`

Explanation

Dispersive power `= (delta_(*V) - delta_(R))/(delta_(Y)) = ((mu_(V) - mu_(R)))/((mu_(Y) - 1)) = ((mu_(V) - 1) - (mu_(R) - 1))/((mu_(Y) - 1))`
We know that, `(1)/(f) = (mu-1) ((1)/(R_(1)) - (1)/(R_(2))) = (mu-1)K` where `K = (1)/(R_(1)) - (1)/(R_(2))`
So, `(mu_(V) - 1)K = (1)/(98) .....(i)`
`(mu_(R) - 1) K = (1)/(100)...(ii)`
and `(mu_(Y) - 1)K = (1)/(99) ...(iii)`
`:.` Dispersice power, `omega = ((1)/(98) - (1)/(100))/((1)/(99)) = (99)/(4900)`